Determining subset of components of an optical characteristic of patterning apparatus

ABSTRACT

A method for determining a component of optical characteristic of a patterning process. The method includes obtaining (i) a plurality of desired features, (ii) a plurality of simulated features based on the plurality of desired features and an optical characteristic of a patterning apparatus, and (iii) a performance metric (e.g., EPE) related to a desired feature of the plurality of desired features and an associated simulated feature of the plurality of simulated features; determining a set of optical sensitivities of the patterning process by computing a change in value of the performance metric based on a change in value of the optical characteristic; and identifying, based on the set of optical sensitivities, a set of components (e.g., principal components) of the optical characteristic that include dominant contributors in changing the value of the performance metric.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT PatentApplication No. PCT/EP2019/084821 which was filed on Dec. 12, 2019,which claims the benefit of priority of U.S. Patent Application No.62/786,642 which was filed on Dec. 31, 2018 and which is incorporatedherein in its entirety by reference.

FIELD

The description herein relates to patterning apparatuses and processes,and more particularly to a method or tool for tuning of an apparatus ofa patterning process, such as optical parameters related to alithographic apparatus.

BACKGROUND

A lithography apparatus is a machine that applies a desired pattern ontoa target portion of a substrate. A lithography apparatus can be used,for example, in the manufacture of devices such as integrated circuits(ICs). In that circumstance, a patterning device (e.g., a mask or areticle) may be used to generate a pattern corresponding to anindividual layer of the device, and this pattern can be transferred ontoa target portion (e.g. comprising part of, one or several dies) on asubstrate (e.g. a silicon wafer) that has, e.g., a layer ofradiation-sensitive material (resist), by methods such as irradiatingthe target portion via a pattern on the patterning device. In general, asingle substrate will contain a plurality of adjacent target portions towhich the pattern is transferred successively by the lithographicapparatus, one target portion at a time. In one type of lithographicapparatus, the pattern on the entire patterning device is transferredonto one target portion in one go; such an apparatus is commonlyreferred to as a stepper. In an alternative apparatus, commonly referredto as a step-and-scan apparatus, a projection beam scans over thepatterning device in a given reference direction (the “scanning”direction) while synchronously moving the substrate parallel oranti-parallel to this reference direction. Different portions of thepattern on the patterning device are transferred to one target portionprogressively. Since, in general, a lithographic projection apparatuswill have a demagnification factor M (generally >1), the speed F atwhich the substrate is moved will be a factor M times that at which theprojection beam scans the patterning device.

Prior to transferring the pattern from the patterning device to thesubstrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of thetransferred pattern. This array of procedures is used as a basis to makean individual layer of a device, e.g., an IC. The substrate may thenundergo various processes such as etching, ion-implantation (doping),metallization, oxidation, chemo-mechanical polishing, etc., all intendedto finish off the individual layer of the device. If several layers arerequired in the device, then the whole procedure, or a variant thereof,is repeated for each layer. Eventually, a device will be present in eachtarget portion on the substrate. These devices are then separated fromone another by a technique such as dicing or sawing, whence theindividual devices can be mounted on a carrier, connected to pins, etc.

Thus, manufacturing devices, such as semiconductor devices, typicallyinvolves processing a substrate (e.g., a semiconductor wafer) using anumber of fabrication processes to form various features and multiplelayers of the devices. Such layers and features are typicallymanufactured and processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apatterning step, such as optical and/or nanoimprint lithography using apatterning device in a lithographic apparatus, to transfer a pattern onthe patterning device to a substrate and typically, but optionally,involves one or more related pattern processing steps, such as resistdevelopment by a development apparatus, baking of the substrate using abake tool, etching using the pattern using an etch apparatus, etc.

SUMMARY

Optical systems can play a role in the performance of a patterningprocess. Accordingly, there is provided herein a technique to enablepatterning process design, modification, control, etc. based on acharacteristic of an optical system of a patterning apparatus such as ascanner.

In an embodiment, there is provided a method for determining a componentof optical characteristic of a patterning process. The method involvesobtaining (i) a plurality of desired features, (ii) a plurality ofsimulated features based on the plurality of desired features and anoptical characteristic of the patterning process, and (iii) aperformance metric related to a desired feature of the plurality ofdesired features and an associated simulated feature of the plurality ofsimulated features; determining a set of optical sensitivities of thepatterning process by computing a change in value of the performancemetric based on a change in value of the optical characteristic; andidentifying, based on the set of optical sensitivities, a set ofcomponents of the optical characteristic that comprise dominantcontributors in changing the value of the performance metric.

In an embodiment, the identifying the set of components of the opticalcharacteristic involves performing a principal component analysis on theset of optical sensitivities; and determining a linear combination ofthe optical characteristic that accounts for substantial variationswithin the set of optical sensitivities.

In an embodiment, the dominant contributors comprise the linearcombination of the optical characteristic.

In an embodiment, the optical characteristic characterizes an opticalaberration of an optical system of the patterning apparatus.

In an embodiment, the optical characteristic is defined via a Zernikepolynomial.

In an embodiment, a component of the set of components of the opticalcharacteristic is a coefficient of the Zernike polynomial.

In an embodiment, the component corresponds to a correctable Zernikecoefficient, wherein the correctable Zernike coefficient is tunable viaan adjustment mechanism of the patterning apparatus.

In an embodiment, the linear combination includes a correctable Zernikecoefficient and a non-correctable Zernike coefficient, wherein thenon-correctable Zernike coefficient is not tunable via an adjustmentmechanism of the patterning apparatus.

In an embodiment, the correctable Zernike coefficient is a low orderZernike coefficient.

Furthermore, in an embodiment, there is provided a method of source maskoptimization based on optical sensitivity of a patterning process. Themethod involves obtaining (i) a set of optical sensitivities, and (ii) aset of components including an optical characteristic that are dominantcontributors to variations in the set of optical sensitivities;determining, via a patterning process model, source pattern or maskpattern based on the set of components including the opticalcharacteristic such that a performance metric of the patterning processis improved.

Furthermore, in an embodiment, there is provided a computer programproduct comprising a non-transitory computer readable medium havinginstructions recorded thereon, the instructions when executed by acomputer system implementing the aforementioned methods.

BRIEF DESCRIPTION OF THE DRAWINGS

The above aspects and other aspects and features will become apparent tothose ordinarily skilled in the art upon review of the followingdescription of specific embodiments in conjunction with the accompanyingfigures, wherein:

FIG. 1 schematically depicts a lithography apparatus, according to anembodiment;

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster, according to an embodiment;

FIG. 3 is a flow chart for modelling and/or simulating parts of apatterning process, according to an embodiment;

FIG. 4 is a flow chart for determining one or more opticalcharacteristic of a patterning apparatus, according to an embodiment;

FIGS. 5A, 5B, 5C, 5D, 5E, 5F, and 5G illustrate different a mask patternor desired patterns to be printed on a wafer, according to anembodiment;

FIG. 6 illustrate a set of optical wavefront sensitivities, according toan embodiment;

FIG. 7A illustrates a wavefront representation of a principle componentcomprising Zernike Z8, according to an embodiment;

FIG. 7B illustrates a bar chart representation of a principal componentcomprising the Zernike Z8 of FIG. 7A, according to an embodiment;

FIG. 7C illustrates a wavefront representation of a principle componentcomprising Zernike Z7, according to an embodiment;

FIG. 7D illustrates a bar chart representing a principal componentcomprising the Zernike Z7 of FIG. 7C, according to an embodiment;

FIG. 7E illustrates a wavefront representation of a principle componentcomprising Zernike Z5, according to an embodiment;

FIG. 7F illustrates a bar chart representing a principal componentcomprising the Zernike Z5 of FIG. 7E, according to an embodiment;

FIG. 7G illustrates a wavefront representation of a principle componentcomprising Zernike Z9, according to an embodiment;

FIG. 7H illustrates a bar chart representing a principal componentcomprising the Zernike Z9 of FIG. 7G, according to an embodiment;

FIGS. 8A and 8B illustrates performance measurement based on contours ofa reference feature and a simulated feature (e.g., resulting fromperturbing optical characteristic), according to an embodiment;

FIG. 9 is an example correction potential of a lithographic apparatus,according to an embodiment;

FIG. 10A is a flow chart of a method of an optimization based on opticalsensitivity of a patterning process, according to an embodiment;

FIG. 10B illustrates field points along a slit of a projection opticsbox, according to an embodiment;

FIG. 11 is a flow diagram illustrating aspects of an example methodologyof joint optimization, according to an embodiment.

FIG. 12 shows an embodiment of another optimization method, according toan embodiment.

FIGS. 13A, 13B and 14 show example flowcharts of various optimizationprocesses, according to an embodiment.

FIG. 15 is a block diagram of an example computer system in whichembodiments can be implemented, according to an embodiment;

FIG. 16 is a schematic diagram of another lithographic projectionapparatus, according to an embodiment;

FIG. 17 is a more detailed view of the apparatus in FIG. 16 , accordingto an embodiment; and

FIG. 18 is a more detailed view of the source collector module of theapparatus of FIG. 16 and FIG. 17 , according to an embodiment.

Embodiments will now be described in detail with reference to thedrawings, which are provided as illustrative examples so as to enablethose skilled in the art to practice the embodiments. Notably, thefigures and examples below are not meant to limit the scope to a singleembodiment, but other embodiments are possible by way of interchange ofsome or all of the described or illustrated elements. Whereverconvenient, the same reference numbers will be used throughout thedrawings to refer to same or like parts. Where certain elements of theseembodiments can be partially or fully implemented using knowncomponents, only those portions of such known components that arenecessary for an understanding of the embodiments will be described, anddetailed descriptions of other portions of such known components will beomitted so as not to obscure the description of the embodiments. In thepresent specification, an embodiment showing a singular component shouldnot be considered limiting; rather, the scope is intended to encompassother embodiments including a plurality of the same component, andvice-versa, unless explicitly stated otherwise herein. Moreover,applicants do not intend for any term in the specification or claims tobe ascribed an uncommon or special meaning unless explicitly set forthas such. Further, the scope encompasses present and future knownequivalents to the components referred to herein by way of illustration.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts an embodiment of a lithographic apparatusLA. The apparatus comprises:

an illumination system (illuminator) IL configured to condition aradiation beam B (e.g. extreme ultra violet (EUV) radiation orelectromagnetic radiation such as UV radiation or DUV);

a support structure (e.g. a mask table) MT constructed to support apatterning device (e.g. a mask) MA and connected to a first positionerPM configured to accurately position the patterning device in accordancewith certain parameters;

a substrate table (e.g. a wafer table) WT (e.g., WTa, WTb or both)constructed to hold a substrate (e.g. a resist-coated wafer) W andconnected to a second positioner PW configured to accurately positionthe substrate in accordance with certain parameters; and a projectionsystem (e.g. a refractive, catoptric or catadioptric projection system)PS configured to project a pattern imparted to the radiation beam B bypatterning device MA onto a target portion C (e.g. comprising one ormore dies and often referred to as fields) of the substrate W, theprojection system supported on a reference frame (RF).

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array or LCDmatrix, or employing a reflective mask).

The illuminator IL receives a beam of radiation from a radiation sourceSO (e.g., a mercury lamp or excimer laser). The radiation source and thelithographic apparatus may be separate entities, for example when theradiation source is an excimer laser. In such cases, the radiationsource is not considered to form part of the lithographic apparatus andthe radiation beam is passed from the radiation source SO to theilluminator IL with the aid of a beam delivery system BD comprising forexample suitable directing mirrors and/or a beam expander. In othercases the radiation source may be an integral part of the apparatus, forexample when the radiation source is a mercury lamp. The radiationsource SO and the illuminator IL, together with the beam delivery systemBD if required, may be referred to as a radiation system.

The illuminator IL may alter the intensity distribution of the beam. Theilluminator may be arranged to limit the radial extent of the radiationbeam such that the intensity distribution is non-zero within an annularregion in a pupil plane of the illuminator IL. Additionally oralternatively, the illuminator IL may be operable to limit thedistribution of the beam in the pupil plane such that the intensitydistribution is non-zero in a plurality of equally spaced sectors in thepupil plane. The intensity distribution of the radiation beam in a pupilplane of the illuminator IL may be referred to as an illumination mode.

So, the illuminator IL may comprise adjuster AM configured to adjust the(angular/spatial) intensity distribution of the beam. Generally, atleast the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. The illuminator IL maybe operable to vary the angular distribution of the beam. For example,the illuminator may be operable to alter the number, and angular extent,of sectors in the pupil plane wherein the intensity distribution isnon-zero. By adjusting the intensity distribution of the beam in thepupil plane of the illuminator, different illumination modes may beachieved. For example, by limiting the radial and angular extent of theintensity distribution in the pupil plane of the illuminator IL, theintensity distribution may have a multi-pole distribution such as, forexample, a dipole, quadrupole or hexapole distribution. A desiredillumination mode may be obtained, e.g., by inserting an optic whichprovides that illumination mode into the illuminator IL or using aspatial light modulator.

The illuminator IL may be operable alter the polarization of the beamand may be operable to adjust the polarization using adjuster AM. Thepolarization state of the radiation beam across a pupil plane of theilluminator IL may be referred to as a polarization mode. The use ofdifferent polarization modes may allow greater contrast to be achievedin the image formed on the substrate W. The radiation beam may beunpolarized. Alternatively, the illuminator may be arranged to linearlypolarize the radiation beam. The polarization direction of the radiationbeam may vary across a pupil plane of the illuminator IL. Thepolarization direction of radiation may be different in differentregions in the pupil plane of the illuminator IL. The polarization stateof the radiation may be chosen in dependence on the illumination mode.For multi-pole illumination modes, the polarization of each pole of theradiation beam may be generally perpendicular to the position vector ofthat pole in the pupil plane of the illuminator IL. For example, for adipole illumination mode, the radiation may be linearly polarized in adirection that is substantially perpendicular to a line that bisects thetwo opposing sectors of the dipole. The radiation beam may be polarizedin one of two different orthogonal directions, which may be referred toas X-polarized and Y-polarized states. For a quadrupole illuminationmode the radiation in the sector of each pole may be linearly polarizedin a direction that is substantially perpendicular to a line thatbisects that sector. This polarization mode may be referred to as XYpolarization. Similarly, for a hexapole illumination mode the radiationin the sector of each pole may be linearly polarized in a direction thatis substantially perpendicular to a line that bisects that sector. Thispolarization mode may be referred to as TE polarization.

In addition, the illuminator IL generally comprises various othercomponents, such as an integrator IN and a condenser CO. Theillumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

Thus, the illuminator provides a conditioned beam of radiation B, havinga desired uniformity and intensity distribution in its cross section.

The support structure MT supports the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a pattern in atarget portion of the substrate. In an embodiment, a patterning deviceis any device that can be used to impart a radiation beam with a patternin its cross-section so as to create a pattern in a target portion ofthe substrate. It should be noted that the pattern imparted to theradiation beam may not exactly correspond to the desired pattern in thetarget portion of the substrate, for example if the pattern includesphase-shifting features or so called assist features. Generally, thepattern imparted to the radiation beam will correspond to a particularfunctional layer in a device being created in the target portion, suchas an integrated circuit.

A patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

The projection system PS has an optical transfer function which may benon-uniform, which can affect the pattern imaged on the substrate W. Forunpolarized radiation such effects can be fairly well described by twoscalar maps, which describe the transmission (apodization) and relativephase (aberration) of radiation exiting the projection system PS as afunction of position in a pupil plane thereof. These scalar maps, whichmay be referred to as the transmission map and the relative phase map,may be expressed as a linear combination of a complete set of basicfunctions. A particularly convenient set is the Zernike polynomials,which form a set of orthogonal polynomials defined on a unit circle. Adetermination of each scalar map may involve determining thecoefficients in such an expansion. Since the Zernike polynomials areorthogonal on the unit circle, the Zernike coefficients may bedetermined by calculating the inner product of a measured scalar mapwith each Zernike polynomial in turn and dividing this by the square ofthe norm of that Zernike polynomial.

The transmission map and the relative phase map are field and systemdependent. That is, in general, each projection system PS will have adifferent Zernike expansion for each field point (i.e. for each spatiallocation in its image plane). The relative phase of the projectionsystem PS in its pupil plane may be determined by projecting radiation,for example from a point-like source in an object plane of theprojection system PS (i.e. the plane of the patterning device MA),through the projection system PS and using a shearing interferometer tomeasure a wavefront (i.e. a locus of points with the same phase). Ashearing interferometer is a common path interferometer and therefore,advantageously, no secondary reference beam is required to measure thewavefront. The shearing interferometer may comprise a diffractiongrating, for example a two dimensional grid, in an image plane of theprojection system (i.e. the substrate table WT) and a detector arrangedto detect an interference pattern in a plane that is conjugate to apupil plane of the projection system PS. The interference pattern isrelated to the derivative of the phase of the radiation with respect toa coordinate in the pupil plane in the shearing direction. The detectormay comprise an array of sensing elements such as, for example, chargecoupled devices (CCDs).

The projection system PS of a lithography apparatus may not producevisible fringes and therefore the accuracy of the determination of thewavefront can be enhanced using phase stepping techniques such as, forexample, moving the diffraction grating. Stepping may be performed inthe plane of the diffraction grating and in a direction perpendicular tothe scanning direction of the measurement. The stepping range may be onegrating period, and at least three (uniformly distributed) phase stepsmay be used. Thus, for example, three scanning measurements may beperformed in the y-direction, each scanning measurement being performedfor a different position in the x-direction. This stepping of thediffraction grating effectively transforms phase variations intointensity variations, allowing phase information to be determined. Thegrating may be stepped in a direction perpendicular to the diffractiongrating (z direction) to calibrate the detector.

The diffraction grating may be sequentially scanned in two perpendiculardirections, which may coincide with axes of a co-ordinate system of theprojection system PS (x and y) or may be at an angle such as 45 degreesto these axes. Scanning may be performed over an integer number ofgrating periods, for example one grating period. The scanning averagesout phase variation in one direction, allowing phase variation in theother direction to be reconstructed. This allows the wavefront to bedetermined as a function of both directions.

The transmission (apodization) of the projection system PS in its pupilplane may be determined by projecting radiation, for example from apoint-like source in an object plane of the projection system PS (i.e.the plane of the patterning device MA), through the projection system PSand measuring the intensity of radiation in a plane that is conjugate toa pupil plane of the projection system PS, using a detector. The samedetector as is used to measure the wavefront to determine aberrationsmay be used.

The projection system PS may comprise a plurality of optical (e.g.,lens) elements and may further comprise an adjustment mechanism AMconfigured to adjust one or more of the optical elements so as tocorrect for aberrations (phase variations across the pupil planethroughout the field). To achieve this, the adjustment mechanism may beoperable to manipulate one or more optical (e.g., lens) elements withinthe projection system PS in one or more different ways. The projectionsystem may have a co-ordinate system wherein its optical axis extends inthe z direction. The adjustment mechanism may be operable to do anycombination of the following: displace one or more optical elements;tilt one or more optical elements; and/or deform one or more opticalelements. Displacement of an optical element may be in any direction (x,y, z or a combination thereof). Tilting of an optical element istypically out of a plane perpendicular to the optical axis, by rotatingabout an axis in the x and/or y directions although a rotation about thez axis may be used for a non-rotationally symmetric aspherical opticalelement. Deformation of an optical element may include a low frequencyshape (e.g. astigmatic) and/or a high frequency shape (e.g. free formaspheres). Deformation of an optical element may be performed forexample by using one or more actuators to exert force on one or moresides of the optical element and/or by using one or more heatingelements to heat one or more selected regions of the optical element. Ingeneral, it may not be possible to adjust the projection system PS tocorrect for apodization (transmission variation across the pupil plane).The transmission map of a projection system PS may be used whendesigning a patterning device (e.g., mask) MA for the lithographyapparatus LA. Using a computational lithography technique, thepatterning device MA may be designed to at least partially correct forapodization.

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate tables WTa, WTb, two or morepatterning device tables, a substrate table WTa and a table WTb belowthe projection system without a substrate that is dedicated to, forexample, facilitating measurement, and/or cleaning, etc.). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure. For example, alignmentmeasurements using an alignment sensor AS and/or level (height, tilt,etc.) measurements using a level sensor LS may be made.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the patterning device and the projection system Immersiontechniques are well known in the art for increasing the numericalaperture of projection systems. The term “immersion” as used herein doesnot mean that a structure, such as a substrate, must be submerged inliquid, but rather only means that liquid is located between theprojection system and the substrate during exposure.

So, in operation of the lithographic apparatus, a radiation beam isconditioned and provided by the illumination system IL. The radiationbeam B is incident on the patterning device (e.g., mask) MA, which isheld on the support structure (e.g., mask table) MT, and is patterned bythe patterning device. Having traversed the patterning device MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder, 2-D encoder or capacitive sensor), the substratetable WT can be moved accurately, e.g. so as to position differenttarget portions C in the path of the radiation beam B. Similarly, thefirst positioner PM and another position sensor (which is not explicitlydepicted in FIG. 1 ) can be used to accurately position the patterningdevice MA with respect to the path of the radiation beam B, e.g. aftermechanical retrieval from a mask library, or during a scan. In general,movement of the support structure MT may be realized with the aid of along-stroke module (coarse positioning) and a short-stroke module (finepositioning), which form part of the first positioner PM. Similarly,movement of the substrate table WT may be realized using a long-strokemodule and a short-stroke module, which form part of the secondpositioner PW. In the case of a stepper (as opposed to a scanner) thesupport structure MT may be connected to a short-stroke actuator only,or may be fixed. Patterning device MA and substrate W may be alignedusing patterning device alignment marks M1, M2 and substrate alignmentmarks P1, P2. Although the substrate alignment marks as illustratedoccupy dedicated target portions, they may be located in spaces betweentarget portions (these are known as scribe-lane alignment marks).Similarly, in situations in which more than one die is provided on thepatterning device MA, the patterning device alignment marks may belocated between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the support structure MT and the substrate table WT arekept essentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the supportstructure MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the support structure MT is kept essentiallystationary holding a programmable patterning device, and the substratetable WT is moved or scanned while a pattern imparted to the radiationbeam is projected onto a target portion C. In this mode, generally apulsed radiation source is employed and the programmable patterningdevice is updated as required after each movement of the substrate tableWT or in between successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2 , the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatuses to perform pre- and post-exposureprocesses on a substrate. Conventionally these include one or more spincoaters SC to deposit one or more resist layers, one or more developersDE to develop exposed resist, one or more chill plates CH and/or one ormore bake plates BK. A substrate handler, or robot, RO picks up one ormore substrates from input/output port I/O1, I/O2, moves them betweenthe different process apparatuses and delivers them to the loading bayLB of the lithographic apparatus. These apparatuses, which are oftencollectively referred to as the track, are under the control of a trackcontrol unit TCU which is itself controlled by the supervisory controlsystem SCS, which also controls the lithographic apparatus vialithography control unit LACU. Thus, the different apparatuses can beoperated to maximize throughput and processing efficiency.

As device manufacturing processes used to manufacture devices such asICs continue to advance, the dimensions of functional elements havecontinually been reduced while the amount of functional elements, suchas transistors, per device has been steadily increasing over decades,following a trend commonly referred to as “Moore's law”. To enable this,some processes aim to create patterns at or below the classicalresolution limit.

The process in which features with dimensions smaller than the classicalresolution limit of a lithographic projection apparatus are printed, iscommonly known as low-k₁ lithography, according to the resolutionformula CD=k₁×λ/NA, where λ is the wavelength of radiation employed(e.g., 193 nm or about 13 nm, e.g., about 13.5 nm), NA is the numericalaperture of projection optics in the lithographic projection apparatus,CD is the “critical dimension”—generally the smallest feature sizeprinted—and k₁ is an empirical resolution factor. In general, thesmaller k₁ the more difficult it becomes to reproduce a pattern on thesubstrate that resembles the shape and dimensions planned by a devicedesigner in order to achieve particular electrical functionality andperformance. To overcome these difficulties, sophisticated fine-tuningsteps are applied to the lithographic projection apparatus and/orpatterning device pattern. These include, for example, but not limitedto, optimization of optical coherence settings, customized illuminationschemes, use of phase shifting patterning devices, optical proximitycorrection (OPC) in the patterning device pattern, optimization of NA,or other methods generally defined as “resolution enhancementtechniques” (RET).

In a lithographic projection apparatus, an illumination system providesillumination (i.e. radiation) to patterning device and projection opticsdirects the illumination from the patterning device onto a substrate. Inan embodiment, the projection optics enables the formation of an aerialimage (AI), which is the radiation intensity distribution on thesubstrate. A resist layer on the substrate is exposed and the aerialimage is transferred to the resist layer as a latent “resist image” (RI)therein. The resist image (RI) can be defined as a spatial distributionof solubility of the resist in the resist layer. In an embodiment,simulation of a lithography process can simulate the production of theaerial image and/or resist image.

An exemplary flow chart for modelling and/or simulating parts of apatterning process is illustrated in FIG. 3 . As will be appreciated,the models may represent a different patterning process and need notcomprise all the models described below.

An illumination model 31 represents optical characteristics (includingradiation intensity distribution and/or phase distribution) of anillumination mode used to generate a patterned radiation beam. Theillumination model 31 can represent the optical characteristics of theillumination that include, but not limited to, numerical aperturesettings, illumination sigma (σ) settings as well as any particularillumination mode shape (e.g. off-axis radiation shape such as annular,quadrupole, dipole, etc.), where σ (or sigma) is outer radial extent ofthe illuminator.

A projection optics model 32 represents optical characteristics(including changes to the radiation intensity distribution and/or thephase distribution caused by the projection optics) of the projectionoptics. The projection optics model 32 may include optical aberrationscaused by various factors, for example, heating of the components of theprojection optics, stress caused by mechanical connections of thecomponents of the projection optics, etc. The projection optics model 32can represent the optical characteristics of the projection optics,including one or more selected from: an aberration, a distortion, arefractive index, a physical size, a physical dimension, an absorption,etc. Optical properties of the lithographic projection apparatus (e.g.,properties of the illumination, the patterning device pattern and theprojection optics) dictate the aerial image. Since the patterning devicepattern used in the lithographic projection apparatus can be changed, itis desirable to separate the optical properties of the patterning devicepattern from the optical properties of the rest of the lithographicprojection apparatus including at least the illumination and theprojection optics. The illumination model 31 and the projection opticsmodel 32 can be combined into a transmission cross coefficient (TCC)model.

A patterning device pattern model 33 represents optical characteristics(including changes to the radiation intensity distribution and/or thephase distribution caused by a given patterning device pattern) of apatterning device pattern (e.g., a device design layout corresponding toa feature of an integrated circuit, a memory, an electronic device,etc.), which is the representation of an arrangement of features on orformed by a patterning device. The patterning device model 33 captureshow the design features are laid out in the pattern of the patterningdevice and may include a representation of detailed physical propertiesof the patterning device and a patterning device pattern, as described,for example, in U.S. Pat. No. 7,587,704, which is incorporated byreference in its entirety.

A resist model 37 can be used to calculate the resist image from theaerial image. An example of such a resist model can be found in U.S.Pat. No. 8,200,468, which is hereby incorporated by reference in itsentirety. The resist model typically describes the effects of chemicalprocesses which occur during resist exposure, post exposure bake (PEB)and development, in order to predict, for example, contours of resistfeatures formed on the substrate and so it typically related only tosuch properties of the resist layer (e.g., effects of chemical processeswhich occur during exposure, post-exposure bake and development). In anembodiment, the optical properties of the resist layer, e.g., refractiveindex, film thickness, propagation and polarization effects—may becaptured as part of the projection optics model 32.

Having these models, an aerial image 36 can be simulated from theillumination model 31, the projection optics model 32 and the patterningdevice pattern model 33. An aerial image (AI) is the radiation intensitydistribution at substrate level. Optical properties of the lithographicprojection apparatus (e.g., properties of the illumination, thepatterning device and the projection optics) dictate the aerial image.

A resist layer on a substrate is exposed by the aerial image and theaerial image is transferred to the resist layer as a latent “resistimage” (RI) therein. The resist image (RI) can be defined as a spatialdistribution of solubility of the resist in the resist layer. A resistimage 38 can be simulated from the aerial image 36 using a resist model37. So, in general, the connection between the optical and the resistmodel is a simulated aerial image intensity within the resist layer,which arises from the projection of radiation onto the substrate,refraction at the resist interface and multiple reflections in theresist film stack. The radiation intensity distribution (aerial imageintensity) is turned into a latent “resist image” by absorption ofincident energy, which is further modified by diffusion processes andvarious loading effects. Efficient simulation methods that are fastenough for full-chip applications approximate the realistic3-dimensional intensity distribution in the resist stack by a2-dimensional aerial (and resist) image.

In an embodiment, the resist image can be used an input to apost-pattern transfer process model 39. The post-pattern transferprocess model 39 defines performance of one or more post-resistdevelopment processes (e.g., etch, CMP, etc.) and can produce apost-etch image.

Thus, the model formulation describes most, if not all, of the knownphysics and chemistry of the overall process, and each of the modelparameters desirably corresponds to a distinct physical or chemicaleffect. The model formulation thus sets an upper bound on how well themodel can be used to simulate the overall manufacturing process.

Simulation of the patterning process can, for example, predict contours,CDs, edge placement (e.g., edge placement error), pattern shift, etc. inthe aerial, resist and/or etched image. Thus, the objective of thesimulation is to accurately predict, for example, edge placement, and/orcontours, and/or pattern shift, and/or aerial image intensity slope,and/or CD, etc. of the printed pattern. These values can be comparedagainst an intended design to, e.g., correct the patterning process,identify where a defect is predicted to occur, etc. The intended designis generally defined as a pre-OPC design layout which can be provided ina standardized digital file format such as GDSII or OASIS or other fileformat.

Details of techniques and models used to transform a patterning devicepattern into various lithographic images (e.g., an aerial image, aresist image, etc.), apply OPC using those techniques and models andevaluate performance (e.g., in terms of process window) are described inU.S. Patent Application Publication Nos. US 2008-0301620, 2007-0050749,2007-0031745, 2008-0309897, 2010-0162197, 2010-0180251 and 2011-0099526,the disclosure of each which is hereby incorporated by reference in itsentirety.

In an embodiment, an optical characteristic of the patterning apparatus(e.g., a scanner) affects the performance of the patterning process. Asmentioned earlier, the optical characteristic may be represented by aZernike polynomial. In an embodiment, the optical characteristic is anoptical aberration of a lens of a projection optics of the patterningapparatus. According to an embodiment, the optical aberration may bedecomposed into multiple components. For example, the optical aberrationmay be decomposed into multiple Zernike coefficients (e.g., Z1-Z37),where each Zernike coefficient is associated with a magnitude value. So,in an embodiment, one or more Zernike coefficients and associatedmagnitude values together determine a value of the optical aberration.

The optical characteristic (e.g., an optical aberration) affects the waya feature (e.g., of a target pattern/desired pattern) will be printed.In an embodiment, one feature may be more sensitive to a particularoptical characteristic (e.g., Z8), while another feature may be moresensitive to a different optical characteristic (e.g., Z9). In anembodiment, optical sensitivities may be determined for a limited set offeatures e.g., corresponding to hot spots or representative features ofa pattern to be printed on a substrate. Evaluating optical sensitivitiesfor limited patterns may be desirable since computation times of thesimulation of the patterning process such as SO, MO, SMO, or otheroptimization process, are relatively high for full chip applicationcompared to for clips. Furthermore, based on the optical sensitivitiesof selected patterns, a limited number of components of opticalcharacteristics is determined to reduce the number of parameters to betuned to improve performance of the patterning process. Thus, any imagetuning recipe based on the tuning parameters will effectively improvethe patterning process with low to minimum tuning of e.g., the opticalcharacteristic.

Example mask patterns M1-M7 and selected features therein areillustrated in FIGS. 5A-5G. In an embodiment, the mask patterns M1-M7may be different portions of a single mask. Each mask pattern (e.g., M1,M2, M3, M4, M5, M6, or M7) includes features corresponding to a part ofa desired circuit, e.g., memory, SRAM, microprocessor, desired to beprinted on a substrate. Within each mask pattern a set of representativefeatures may be selected for which an optical sensitivity may bedetermined. According to an embodiment, the selected features arecontained within a unit cell that serves as a desired portion (e.g., hotspots or representative portion) of the mask. For example, a first unitcell 510 of mask pattern M1 includes three features, a second unit cell520 of mask pattern M2 includes seven features, a third unit cell 530 ofmask pattern M3 includes four features, a fourth unit cell 540 of maskpattern M4 includes two features, a fifth unit cell 550 of mask patternM5 includes two features, a sixth unit cell 560 of mask pattern M6includes two features, and a seventh unit cell 570 of mask pattern M7includes two features. It can be seen that the features in a unit cell(e.g., 510) have features of similar geometric characteristic such asshape and size and placed at equidistance relative to each other. Inanother unit cell (e.g., 530), the features have different geometriccharacteristic such as sizes, as well as the features may be placed atdifferent distances relative to each other.

In an embodiment, such different layouts of features within a unit cellwill result in different optical sensitivities. Optical sensitivityrelates to a lithographic effect such as an output of a patterningprocess simulation (e.g., edge placement, CD, line placement, etc.) withan aberration (or wavefront) change. Thus the optical sensitivities canbe represented by a sensitivity vector (e.g., d(edgeplacement)/d(Zernike number)), or a sensitivity wavefront (e.g., d(edgeplacement)/d(wavefront pixel)).

Depending on how many unit cells and the features therein are evaluated,a large number of optical sensitivity values may be obtained.Furthermore, the features within the unit cell are sensitive to dose andfocus values. Thus, in an embodiment, thousands of optical sensitivitiesmay be obtained that cannot possibly be individually tuned to improvethe performance of the patterning process. Thus, according to thepresent disclosure, a method 400, a subset of components of the opticalcharacteristics is determined that may be tuned to improve theperformance of the patterning process.

FIG. 4 is a method 400 of determining one or more components comprisingthe optical characteristic (e.g., optical sensitivity or Zernikecoefficient corresponding to an optical sensitivity) of a patterningapparatus that primarily affect the performance of the patterningprocess. In an embodiment, Zernike coefficients approximate an opticalwavefront, and further a full wavefront can be approximated by an innerproduct of the Zernike coefficients with the Zernike polynomials. In anembodiment, optical sensitivities describe how an edge placement isaffected by specific Zernikes or a specific wavefront. So, opticalsensitivities correspond to a sensitivity vector (or map), where theinner product of the sensitivity vector with the Zernike coefficientsdescribes an expected edge placement. Similarly, taking the innerproduct of the wavefront sensitivity map with an actual wavefront,returns the expected edge placement.

In an embodiment, the method 400 determines components comprising theoptical characteristic (e.g., optical sensitivity or Zernike coefficientcorresponding to an optical sensitivity). The optical sensitivitydetermines how edges of a feature of a pattern are affected uponintroducing, for example, an optical aberration during the patterningprocess. Then, according to an embodiment, the number of opticalsensitivities are reduced by a factorization technique that describesthe cross-covariance between datasets, for example, a “principlecomponent analysis” (PCA). For example, PCA identifies a linearcombination of optical characteristics that explains the major variationin the optical sensitivities. Thus, the optical sensitivities can becharacterized by one or more principle components (e.g., P1, P2, P3,etc. comprising linear combinations of optical characteristics such asd/d(Z5), d/d(Z8), d/d(Z7), d/d(Z9), d/d(Z11), etc. sensitivitycoefficients). Based on the identified components, the method can beused for a source optimization, a mask optimization, a source maskoptimization process, or optimization of other process. Examples ofoptimization process are discussed with respect to FIG. 11 -FIG. 14 .

The method 400, in process P42 involves obtaining (i) a plurality ofdesired features 401, (ii) a plurality of simulated features 403 basedon the plurality of desired features 401 and an optical parameter of apatterning apparatus, and (iii) a performance metric 405 related to adesired feature of the plurality of desired features 401 and anassociated simulated feature of the plurality of simulated features 403.In an embodiment, a performance metric 405 is a characteristic of afeature of a substrate and/or the patterning process. In an embodiment,the performance metric 405 is at least one of an edge placement error,critical dimension, a displacement between edges of two features on asubstrate, and/or other commonly known lithography related performancemetric 405.

In an embodiment, the plurality of desired features 401 are selectedfrom one or more portions of a mask pattern such as discussed withrespect to FIGS. 5A-5G. In an embodiment, the obtaining the plurality ofdesired features 401 involves simulating a patterning process modelassuming ideal optical characteristic (e.g., no optical aberrations) andperturbing values of a process parameter. For example, a design layoutor a mask pattern may be used to simulate patterns on the substrate,thereby obtaining the desired features 401 on the substrate.Accordingly, the patterning process model includes an ideal optics modelwhere values of optical aberration may be zero, and only values ofprocess parameters may be changed. In an embodiment, the processparameter is at least one of dose and/or focus whose values may bevaried during the simulation. For example, optical sensitivities areobtained under different process conditions like different dose andfocus values.

In an embodiment, the desired features 401 may be a target pattern or adesign layout. A desired feature of the plurality of desired features401 serves as a reference for determining a performance of thepatterning apparatus or the patterning process. For example, the desiredfeature may be compared with a printed feature on a substrate or apredicted feature that are affected by imperfections (e.g., opticalaberrations) of the patterning apparatus or the patterning process. Inan embodiment, improving the performance of the patterning processinvolves comparing a real or predicted feature with the desired featureor the reference feature.

The obtaining the plurality of simulated features 403 involvessimulating the patterning process model perturbing the opticalparameter, and the values of the process parameter to obtain a pluralityof simulated features 403 associated with each of the plurality ofdesired features 401. In an embodiment, the process parameter is atleast one of dose and/or focus whose values may be varied during thesimulation. Furthermore, the values of the dose and focus used duringthe simulation are similar to that used for obtaining the desiredfeature or reference feature.

As mentioned earlier, a desired feature of the plurality of desiredfeature and an associated simulated feature of the plurality ofsimulated feature may be compared to obtain the performance metric 405(e.g., EPE) of the patterning process. For example, EPE between thedesired feature and the simulated feature may be determined. In anembodiment, the EPE may be determined in a particular direction such asin horizontal and vertical direction as illustrated in FIGS. 8A and 8B.

Referring back to FIG. 4 , the method 400, in process P44 involvesdetermining a set of optical sensitivities 440 of the patterning processby computing a change in value of the performance metric 405 based on achange in value of the optical parameter. In an embodiment, an opticalsensitivity of the patterning process is a differential of theperformance metric 405 with respect to a Zernike coefficient.Accordingly, a set of optical sensitivities 440 can be obtained bytaking a differential of the performance metric 405 with each of theZernike coefficient.

In an embodiment, the determining of the change in the performancemetric 405 involves overlapping the desired feature and the simulatedfeature; and measuring a difference in a pre-determined directionbetween overlapping contours of the desired feature and the simulatedfeature. In an embodiment, the difference is measured in a horizontaldirection and/or a vertical direction. Then, the performance metric 405becomes the EPE along a x-direction and y-direction.

In FIGS. 8A and 8B, a desired feature 810 (also referred as a targetfeature 810) and a simulated feature 820 are overlapped to determine adifference between contours of the overlapping features 810 and 820. Asmentioned earlier, feature 810 can be a desired feature obtained viasimulation or a design feature of a design layout. The feature 820 is anexample of the simulated feature which is distorted compared to theassociated desired feature due to, for example, the perturbation invalues of the optical aberration (e.g., magnitude of the Zernikecoefficient) of the patterning apparatus.

In an embodiment, the difference is computed along a vertical directionand/or horizontal direction. For example, along cut lines CLy and CLx inFIG. 8A. In an embodiment, difference is a positive when the edge of 820moves outward with respect to 810 and negative when the edge of 820moves inwards with respect to 810. Then, the differences along they-direction are y12 (e.g., 0.1 nm) between points 1 and 2, and y34(e.g., 0.2 nm) between points 3 and 4. Similarly, the differences alongthe x-direction are x12 between points 1 and 2, and x34 between points 3and 4. In an embodiment, the difference can be a sum of difference in aparticular direction.

In an embodiment, as shown in FIG. 8B, a difference may be computedalong an inclined cut line CL3. In an embodiment, the differences alongthe inclined cut lines may be resolved in x-component (along x-axis) andy-component (along y-axis) using simple trigonometric relationship.Then, the x-differences and y-difference may be used further, forexample, during the PCA. Such difference in edges is referred as EPE,which may be used as the performance metric 405.

When the edge placement error is used as the performance metric 405 andthe optical characteristic is defined by a Zernike polynomial, then anoptical sensitivity vector of the patterning process is computed usingfollowing differential equation:

${{optical}\mspace{14mu}{sensitivity}} = \frac{\partial{EPE}_{k}}{\partial Z_{n}}$

In above equation Z_(n) is the nth Zernike (e.g., Z2, Z3, Z4, Z5, Z6,Z7, Z8, Z9, etc.), and EPE_(k) is k-th edge placement errorcorresponding to the n-th Zernike. An example of optical sensitivities440 based on above equation is illustrated in FIG. 6 . For example, ifthe simulation involves 41 clips, 2 edges of a feature, 5 focus levels,and 3 dose levels, then a total of 1230 optical sensitivity vectors areobtained. Furthermore, most imaging metrics that characterize thefeature of a substrate scale linearly with optical sensitivities. Forexample, a lithographic metric may be computed as follows. Wheresensitivity is determined based on the performance metric 405, asdiscussed above. In an embodiment, a litho metric may be computed basedon a linear combination of sensitivity values (e.g., a differential of aperformance metric) and the corresponding Zernike coefficient (Z_(k)).Litho metric=Σ_(k)Sensitivity_(k) ·Z _(k)

The method 400, in process P46 involves identifying, based on the set ofoptical sensitivities 440, a set of components 460 including the opticalcharacteristics that are dominant contributors in changing the value ofthe performance metric 405. In an embodiment, a component(interchangeably referred as an optical component) is the opticalcharacteristic can be described via is a Zernike coefficient, so a setof components 460 including the optical characteristics can be describedvia a set of Zernike coefficients. For example, the set of components460 (e.g., P1, P2, P3, etc.) includes relatively large contributionsfrom Z8, Z11, Z15, Z20 and Z24, which combined explains most of thevariation in the optical sensitivity values within the set of opticalsensitivities 440 computed above. In other words, the set of components460 (P1, P2, P3, etc. including relatively large contributions from Z8,Z11, Z15, Z20 and Z24) are the dominant contributors in changing thevalue of the performance metric 405. Thus, in an embodiment, only someof the optical characteristics (e.g., including contributions from Z5,Z8, etc.) of the set of components 460 may be tuned to improve theperformance of the patterning process.

In an embodiment, the process P46 of the identifying the set ofcomponents 460 comprising the optical characteristics involvesperforming a principal component analysis on the set of opticalsensitivities 440; and determining a linear combination of the opticalcharacteristics that accounts for substantial variations within the setof optical sensitivities 440. Such linear combination is referred as aprincipal component of the set of optical sensitivities 440. Forexample, a principal component is a linear combination of d/d(Z8),d/d(Z11), d/d(Z15), d/d(Z20) and d/d(Z24). Thereby, modifying values ofone or more of the (optical) characteristics (e.g., Z4, Z5, Z8) withinthe linear combination is sufficient to improve the performance of thepatterning process. For example, the characteristic (e.g., Z8) that isthe most significant contributor within a principal component (e.g.,P1).

In an embodiment, a plurality of principal components (e.g., 3 or 4components, P1-P4) are identified that together explain, for example,more than 90% of the variation in the optical sensitivities 440. In anembodiment, the principal components may be identified based on othercriteria such as a covariance matrix that determined covariance based onprincipal components having same variables (e.g., Z8). Thus, theprincipal components reduce number of variables (e.g., opticalparameters related to the optical aberrations) to be adjusted to aselected few that explains most of the variation, or fulfil othercriteria such as co-variance used in PCA. For example, the 1230 opticalsensitivities of FIG. 6 can be reduced to four principal components thatexplain 90% of the variation in the performance. The four exampleprincipal components are illustrated in FIGS. 7B, 7D, 7F, and 7H.Furthermore, within the principal components, a wavefront sensitivitymap of a lower order Zernike that explains most variation is illustratedin FIGS. 7A, 7C, 7E, and 7F.

In an embodiment, a lower order Zernike coefficient such as Z2-Z9 (oroptical characteristic in general) may be desired to be part of adominant contribution, since such lower order Zernike can be modifiedvia adjusting mechanism (e.g., connected to one or more mirrors) toadjust the performance of the patterning process. Thus, having any lowerorder Zernike in the principal component that can account for mostvariation may be particularly advantageous, since modifying for onecomponent (e.g., Z8) will help offset impact of other higher ordercomponents (e.g., Z11, Z15, Z20, etc.) within the linear combination ofthe principal component. In an embodiment, ability to correct for higherorder Zernike is highly desired since the patterning apparatus may benot have correction potential for higher order Zernikes. For example,impact of only lower order Zernikes are correctable (e.g., viaadjustment mechanism of mirrors), as presented in example correctionpotential relationship in FIG. 9 . For example, a constant Z2 indicatesa translation of the substrate table in the x-direction, a constant Z3indicates a translation of the substrate table in the y-direction, aconstant Z4 is mainly indicative of a translation of the substrate tablein the z-direction. Thus all can be compensated without any mirrormovement. Similarly, Z5, Z7 and Z8 may be used for as offsets of thesubstrate table.

In an embodiment, a performance impact due to the higher ordercomponents may not be directly correctable. In other words, no tuningknobs or adjustment mechanism is available to correct for the impact ofthe higher order optical component (e.g., higher order opticalaberrations). Thus, identifying one or more optical components (e.g.,Z8, Z7, etc.) that can account for maximum variation, as well ascompensate for effects of higher order non-correctable opticalcomponents is particular beneficial to improve performance with minimumtuning effort.

In an embodiment, a first principal component PC1 is illustrated in FIG.7B that includes the impact of a lower order Zernike coefficient Z8,which is the largest contributor and can thus be used as a correctionknob. The first principal component PC1 comprises a linear combinationof several Zernike coefficients having different magnitudes. Forexample, the first principal component PC1 comprises a linearcombination: 0.8*Z8−0.4*Z11−0.1*Z15+0.2*Z20. In an embodiment, the firstprincipal component PC1 corresponds to the performance metric EPEy whichis measured along the y-direction (e.g., cut line CLy in FIG. 8A). Inthe specific case of FIG. 7 , all holes of FIG. 5 were used. So PC1relates to the EPEy placements of all holes from FIG. 5 .

Thus, by tuning for Zernike Z8, the feature's behavior or movement alongy-direction may be adjusted. FIG. 7A illustrates a wavefront sensitivitymap of the first principle component P1 that can account for, e.g.,approximately 34% of the variation in the optical sensitivities or therelated performance metric (e.g., EPE). Upon modifying parameters (e.g.,orientation of mirrors) one can minimize the part of the wavefront whichis described by FIG. 7A (the first principle component), one can accountfor performance variations due to Z11, Z15 and Z20 (that have very lowcorrectable potential or are non-correctable, according to FIG. 9 )thereby improving the performance of the patterning process.

In an embodiment, a second principal component PC2 is illustrated inFIG. 7D that includes the impact of a lower order Zernike coefficientZ7, which is the largest contributor and can thus be used as acorrection knob. The second principal component PC2 also comprises alinear combination of several Zernike coefficients having differentmagnitudes. For example, the second principal component PC2 comprises alinear combination: 0.9*Z7+0.4*Z10+0.1*Z14+0.2*Z23+ . . . . In anembodiment, the second principal component PC2 corresponds to theperformance metric EPEx which is measured along the x-direction (e.g.,cut line CLx in FIG. 8A). In the specific case of FIG. 7 , all holes ofFIG. 5 were used. So PC1 relates to the EPEx placements of all holesfrom FIG. 5 .

Thus, by tuning for Zernike Z7, the feature's behavior or movement alongx-direction may be adjusted. FIG. 7C illustrates a wavefront sensitivitymap of the second principle component that can account for, e.g.,approximately 26% of the variation in the optical sensitivities or therelated performance metric (e.g., EPE). Upon modifying parameters (e.g.,orientation of mirrors) one can minimize the part of the wavefront whichis described by FIG. 7B (the second principle component), one canaccount for performance variations due to Z10, Z14, Z23, etc. (that havevery low correctable potential or are non-correctable, according to FIG.9 ) thereby improving the performance of the patterning process.

Similar to the first principal component PC1 and the second principalcomponent PC2, a third principal component PC3 (in FIG. 7F) and a fourthprincipal component PC4 (in FIG. 7H) may be obtained. For example, thethird principal component PC3 comprises a correctable Zernikecoefficient Z5, which can be used to correct for impact due to otherZernike such as Z9 and Z12 (that have low to no correction potential)within the linear combination of PC3. Similarly, the fourth principalcomponent PC4 comprises a correctable Zernike coefficient Z9, which canbe used to correct for impact due to other non-correctable Zernike suchas Z12, Z16 or other Zernike within the linear combination of PC4.

In sum, upon adjusting total lens (e.g., finding the optimal mirrorpositions and tilts), with the lack of any process knowledge, oneminimizes the wavefront aberrations. In an embodiment, the wavefrontaberrations are minimized by minimizing the sum of squared Zernikecoefficients. This is equivalent in minimizing the sum of the squaredwavefront, since the Zernike polynomials for an orthogonal and completeexpansion. So going from the wavefront to the Zernike coefficients is ahuge reduction of data without loosing the relevant content.

According to the methods of the present disclosure, the Zernikecoefficients are mapped onto a new (orthogonal) basis i.e., principlecomponents. In an embodiment, within the EPE space (all possible edgeplacements in different orientations and under different conditions(focus & dose), these principle components for an orthogonal andcomplete set. So going from the sensitivities of all features to only afew dominant components is a huge data reduction, without loss of muchinformation. Combining both makes it possible to optimized the lens byminimizing the sum of squared principle components.

In an embodiment, the process P46 provides values of the identifiedcomponents of the optical characteristic that correspond to acorrectable Zernike coefficient, where the correctable Zernikecoefficient is tunable via an adjustment mechanism of the patterningapparatus. In an embodiment, the linear combination includes acorrectable Zernike coefficient and a non-correctable Zernikecoefficient, where the non-correctable Zernike coefficient is nottunable via an adjustment mechanism of the patterning apparatus.

Once, the optical components that can account for most of the variation(e.g., more than 90% variation) in the performance value of thepatterning process (e.g., related to a feature shape or size), themethod 400, in process P48, further includes adjusting, via an adjustingmechanism, one or more mirrors of the patterning apparatus based on theset of identified optical components to improve a performance metric ofthe patterning process.

In an embodiment, the adjusting the one or more mirrors includesobtaining an optical correction potential of the patterning apparatus,where the correction potential is a relationship between Zernikecoefficients and orders that are correctable or non-correctable via theadjusting mechanism of the patterning apparatus. Further, based on thecorrection potential, one or more mirrors of the optical system of thepatterning apparatus are identified that associated with the correctableZernike coefficients within the set of optical component. Once themirrors are identified, adjusting process involves manipulating theidentified mirrors to compensate for effects of the non-correctableZernike coefficients such that the performance metric of the patterningprocess is improved.

The above method has several applications including source optimization,mask optimization, source mask optimization, or other process parameteroptimization. For example, based on the set of optical sensitivities anda subset of correctable optical components (e.g., within PC1, PC2, PC3,PC4, etc.), an illumination mode, mask pattern, etc. may be modified. Inan embodiment, the optimization process involves determining values ofdesign variables (e.g., mask related, dose values, focus values, etc.)based on reducing of a cost function. An example of the optimizationprocess is discussed in FIG. 10A and FIGS. 11-14 below.

Referring to FIG. 10A, there is provided a method of an optimizationbased on optical sensitivity of a patterning process. The method, inprocess P101, involves obtaining (i) a set of optical sensitivities1001, and (ii) a set of optical components 1003 (e.g., components 460 ofFIG. 4 such as elements of a principal component) that are a dominantcontributor to variations in the set of optical sensitivities

The method, in process P103, involves determining, via a patterningprocess model, source pattern 1030 or mask pattern 1031 based on the setof optical components 1003 such that the performance metric is improved.In an embodiment, the determining the source pattern or the mask patternis an iterative process. An iteration includes simulating the patterningprocess model with the set of values of the optical parameter andperturbing a parameter related to the source pattern and/or the maskpattern, determining the performance metric based on the simulationresults, and determining values of the parameter related to the sourcepattern and/or the mask pattern such that the performance metric isimproved. In an embodiment, the parameter of the source model is atleast one of an illumination mode, and intensity. In an embodiment, theparameter of the mask model is at least one of: a placement location ofan assist feature, a size of the feature, a shape of the assist feature,and/or a distance between two assist features.

In an embodiment, the performance metric is an edge placement error, andthe improving of the performance metric comprises minimizing the edgeplacement error.

In an embodiment, the patterning process model is a source model, a maskmodel, an optics model, a resist model, and/or an etch model. An exampleof the simulation of the patterning process including one or more theaforementioned process models is discussed in FIG. 3 , earlier.

In an embodiment, the method may be further extended to perform lensoptimization, based on a lens optimization merit function. In anembodiment, the lens optimization merit function is based on theprincipal components (e.g., FIGS. 7A-7H) of the optical parameters thatare identified, e.g., in the process P46. An example, lens optimizationmerit function (S) is give in equation below:S=Σ _(i)Σ_(k)(w _(k) ·ΔZ _(k,i))²+Σ_(i)Σ_(m) w _(m)·(Σ_(k) PC _(m,k) ·ΔZ_(k,i))²

In the above equation, a 1^(st) part of the equation is a weight basedZernike term, and a 2^(nd) part is an additional term comprising theprincipal components (e.g., as discussed with respect to FIG. 4 andFIGS. 7B, 7D, 7F, 7H). Furthermore, i runs over various field points1010, (see FIG. 10B) of a slit, k runs over the different Zernikecoefficients (2 till 25, 36, 49, 64 or 100), AZ corresponds to thedifference between a measured Zernike coefficient and a lens modelinduced Zernike coefficient (e.g., induced for simulation purposes),PC_(m,n) is a transformation of the m^(th) principle component toZernike n, and w_(m) is the associated principle component weight.

In an embodiment, the method may further include printing a pattern onthe substrate using the tunable characteristic (e.g., lower orderZernike coefficients within a principal component). Further, measurementdata of the printed pattern may be obtained and the performance of thepatterning apparatus (e.g., a scanner) may be verified against areference performance based on the measurement data.

The method, according to the present disclosure, has several advantages.For example, natural variation of non-adjustable parameters can causelarge performance variation with respect to a desired specification.Such variation may be reduced by adjusting only selected opticalparameters according to the present disclosure. When the cause ofperformance mismatch is a non-tunable optical characteristic, areplacement of hardware related to the non-tunable characteristic causemay be required. However, according to the present disclosure, if anon-tunable characteristic exists, tuning a single or multiple scannerknobs to compensate for the non-tunable characteristic can be proposed.Accordingly, in an embodiment, a non-tunable characteristic (e.g. higherorder Zernike coefficients) can be corrected for by a tuning a tunablecharacteristic (e.g., lower order Zernike coefficients within aprincipal component) of the scanner.

As discussed in method 400, the identified optical characteristic may beemployed in optimization of patterning process or adjusting parametersof the patterning process. As an example, OPC addresses the fact thatthe final size and placement of an image of the design layout projectedon the substrate will not be identical to, or simply depend only on thesize and placement of the design layout on the patterning device. It isnoted that the terms “mask”, “reticle”, “patterning device” are utilizedinterchangeably herein. Also, person skilled in the art will recognizethat, especially in the context of lithography simulation/optimization,the term “mask”/“patterning device” and “design layout” can be usedinterchangeably, as in lithography simulation/optimization, a physicalpatterning device is not necessarily used but a design layout can beused to represent a physical patterning device. For the small featuresizes and high feature densities present on some design layout, theposition of a particular edge of a given feature will be influenced to acertain extent by the presence or absence of other adjacent features.These proximity effects arise from minute amounts of radiation coupledfrom one feature to another and/or non-geometrical optical effects suchas diffraction and interference. Similarly, proximity effects may arisefrom diffusion and other chemical effects during post-exposure bake(PEB), resist development, and etching that generally followlithography.

In order to ensure that the projected image of the design layout is inaccordance with requirements of a given target circuit design, proximityeffects need to be predicted and compensated for, using sophisticatednumerical models, corrections or pre-distortions of the design layout.The article “Full-Chip Lithography Simulation and Design Analysis—HowOPC Is Changing IC Design”, C. Spence, Proc. SPIE, Vol. 5751, pp 1-14(2005) provides an overview of current “model-based” optical proximitycorrection processes. In a typical high-end design almost every featureof the design layout has some modification in order to achieve highfidelity of the projected image to the target design. Thesemodifications may include shifting or biasing of edge positions or linewidths as well as application of “assist” features that are intended toassist projection of other features.

Application of model-based OPC to a target design involves good processmodels and considerable computational resources, given the many millionsof features typically present in a chip design. However, applying OPC isgenerally not an “exact science”, but an empirical, iterative processthat does not always compensate for all possible proximity effect.Therefore, effect of OPC, e.g., design layouts after application of OPCand any other RET, need to be verified by design inspection, i.e.intensive full-chip simulation using calibrated numerical processmodels, in order to minimize the possibility of design flaws being builtinto the patterning device pattern. This is driven by the enormous costof making high-end patterning devices, which run in themulti-million-dollar range, as well as by the impact on turn-around timeby reworking or repairing actual patterning devices once they have beenmanufactured.

Both OPC and full-chip RET verification may be based on numericalmodeling systems and methods as described, for example in, U.S. patentapplication Ser. No. 10/815,573 and an article titled “OptimizedHardware and Software For Fast, Full Chip Simulation”, by Y. Cao et al.,Proc. SPIE, Vol. 5754, 405 (2005).

One RET is related to adjustment of the global bias of the designlayout. The global bias is the difference between the patterns in thedesign layout and the patterns intended to print on the substrate. Forexample, a circular pattern of 25 nm diameter may be printed on thesubstrate by a 50 nm diameter pattern in the design layout or by a 20 nmdiameter pattern in the design layout but with high dose.

In addition to optimization to design layouts or patterning devices(e.g., OPC), the illumination source can also be optimized, eitherjointly with patterning device optimization or separately, in an effortto improve the overall lithography fidelity. The terms “illuminationsource” and “source” are used interchangeably in this document. Sincethe 1990s, many off-axis illumination sources, such as annular,quadrupole, and dipole, have been introduced, and have provided morefreedom for OPC design, thereby improving the imaging results, As isknown, off-axis illumination is a proven way to resolve fine structures(i.e., target features) contained in the patterning device. However,when compared to a traditional illumination source, an off-axisillumination source usually provides less radiation intensity for theaerial image (AI). Thus, it becomes desirable to attempt to optimize theillumination source to achieve the optimal balance between finerresolution and reduced radiation intensity.

Numerous illumination source optimization approaches can be found, forexample, in an article by Rosenbluth et al., titled “Optimum Mask andSource Patterns to Print A Given Shape”, Journal of Microlithography,Microfabrication, Microsystems 1(1), pp. 13-20, (2002). The source ispartitioned into several regions, each of which corresponds to a certainregion of the pupil spectrum. Then, the source distribution is assumedto be uniform in each source region and the brightness of each region isoptimized for process window. However, such an assumption that thesource distribution is uniform in each source region is not alwaysvalid, and as a result the effectiveness of this approach suffers. Inanother example set forth in an article by Granik, titled “SourceOptimization for Image Fidelity and Throughput”, Journal ofMicrolithography, Microfabrication, Microsystems 3(4), pp. 509-522,(2004), several existing source optimization approaches are overviewedand a method based on illuminator pixels is proposed that converts thesource optimization problem into a series of non-negative least squareoptimizations. Though these methods have demonstrated some successes,they typically require multiple complicated iterations to converge. Inaddition, it may be difficult to determine the appropriate/optimalvalues for some extra parameters, such as y in Granik's method, whichdictates the trade-off between optimizing the source for substrate imagefidelity and the smoothness requirement of the source.

For low k₁ photolithography, optimization of both the source andpatterning device is useful to ensure a viable process window forprojection of critical circuit patterns. Some algorithms (e.g. Socha et.al. Proc. SPIE vol. 5853, 2005, p. 180) discretize illumination intoindependent source points and mask into diffraction orders in thespatial frequency domain, and separately formulate a cost function(which is defined as a function of selected design variables) based onprocess window metrics such as exposure latitude which could bepredicted by optical imaging models from source point intensities andpatterning device diffraction orders. The term “design variables” asused herein comprises a set of parameters of a lithographic projectionapparatus or a lithographic process, for example, parameters a user ofthe lithographic projection apparatus can adjust, or imagecharacteristics a user can adjust by adjusting those parameters. Itshould be appreciated that any characteristics of a lithographicprojection process, including those of the source, the patterningdevice, the projection optics, and/or resist characteristics can beamong the design variables in the optimization. The cost function isoften a non-linear function of the design variables. Then standardoptimization techniques are used to minimize the cost function.

Relatedly, the pressure of ever decreasing design rules have drivensemiconductor chipmakers to move deeper into the low k₁ lithography erawith existing 193 nm ArF lithography. Lithography towards lower k₁ putsheavy demands on RET, exposure tools, and the need for litho-friendlydesign. 1.35 ArF hyper numerical aperture (NA) exposure tools may beused in the future. To help ensure that circuit design can be producedon to the substrate with workable process window, source-patterningdevice optimization (referred to herein as source-mask optimization orSMO) is becoming a significant RET for 2×nm node.

A source and patterning device (design layout) optimization method andsystem that allows for simultaneous optimization of the source andpatterning device using a cost function without constraints and within apracticable amount of time is described in a commonly assignedInternational Patent Application No. PCT/US2009/065359, filed on Nov.20, 2009, and published as WO2010/059954, titled “Fast Freeform Sourceand Mask Co-Optimization Method”, which is hereby incorporated byreference in its entirety.

Another source and mask optimization method and system that involvesoptimizing the source by adjusting pixels of the source is described ina commonly assigned U.S. patent application Ser. No. 12/813,456, filedon Jun. 10, 2010, and published as U.S. Patent Application PublicationNo. 2010/0315614, titled “Source-Mask Optimization in LithographicApparatus”, which is hereby incorporated by reference in its entirety.

In a lithographic projection apparatus, as an example, a cost functionis expressed as

$\begin{matrix}{{{CF}( {z_{1},z_{2},\ldots\;,z_{N}} )} = {\sum\limits_{p = 1}^{P}\;{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\;,z_{N}} )}}}} & ( {{Eq}.\mspace{14mu} 1} )\end{matrix}$wherein (z₁, z₂, . . . , z_(N)) are N design variables or valuesthereof. ƒ_(p) (z₁, z₂, . . . , z_(N)) can be a function of the designvariables (z₁, z₂, . . . , z_(N)) such as a difference between an actualvalue and an intended value of a characteristic at an evaluation pointfor a set of values of the design variables of (z₁, z₂, . . . , z_(N)).w_(p) is a weight constant associated with ƒ_(p) (z₁, z₂, . . . ,z_(N)). An evaluation point or pattern more critical than others can beassigned a higher w_(p) value. Patterns and/or evaluation points withlarger number of occurrences may be assigned a higher w_(p) value, too.Examples of the evaluation points can be any physical point or patternon the substrate, any point on a virtual design layout, or resist image,or aerial image, or a combination thereof. ƒ_(p) (z₁, z₂, . . . , z_(N))can also be a function of one or more identified optical characteristicssuch as the LWR, which are functions of the design variables (z₁, z₂, .. . , z_(N)). The cost function may represent any suitablecharacteristics of the lithographic projection apparatus or thesubstrate, for instance, failure rate of a feature, an identifiedoptical characteristic, focus, CD, image shift, image distortion, imagerotation, stochastic effects, throughput, CDU, or a combination thereof.CDU is local CD variation (e.g., three times of the standard deviationof the local CD distribution). CDU may be interchangeably referred to asLCDU. In one embodiment, the cost function represents (i.e., is afunction of) CDU, throughput, and the stochastic effects. In oneembodiment, the cost function represents (i.e., is a function of) EPE,throughput, and the stochastic effects. In one embodiment, the designvariables (z₁, z₂, . . . , z_(N)) comprise dose, global bias of thepatterning device, shape of illumination from the source, or acombination thereof. Since it is the resist image that often dictatesthe circuit pattern on a substrate, the cost function often includesfunctions that represent some characteristics of the resist image. Forexample, ƒ_(p) (z₁, z₂, . . . , z_(N)) of such an evaluation point canbe simply a distance between a point in the resist image to an intendedposition of that point (i.e., edge placement error EPE_(p)(z₁, z₂, . . ., z_(N))). The design variables can be any adjustable parameters such asadjustable parameters of the source, the patterning device, theprojection optics, dose, focus, etc. The projection optics may includecomponents collectively called as “wavefront manipulator” that can beused to adjust shapes of a wavefront and intensity distribution and/orphase shift of the irradiation beam. The projection optics preferablycan adjust a wavefront and intensity distribution at any location alongan optical path of the lithographic projection apparatus, such as beforethe patterning device, near a pupil plane, near an image plane, near afocal plane. The projection optics can be used to correct or compensatefor certain distortions of the wavefront and intensity distributioncaused by, for example, the source, the patterning device, temperaturevariation in the lithographic projection apparatus, thermal expansion ofcomponents of the lithographic projection apparatus. Adjusting thewavefront and intensity distribution can change values of the evaluationpoints and the cost function. Such changes can be simulated from a modelor actually measured. Of course, CF (z₁, z₂, . . . , z_(N)) is notlimited the form in Eq. 1. CF (z₁, z₂, . . . , z_(N)) can be in anyother suitable form.

It should be noted that the normal weighted root mean square (RMS) ofƒ_(p) (z₁, z₂, . . . , z_(N)) is defined as

$\sqrt{\frac{1}{P}{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}}},$therefore, minimizing the weighted RMS of ƒ_(p) (z₁, z₂, . . . , z_(N))is equivalent to minimizing the cost function

${{C{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}} = {\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}}},$defined in Eq. 1. Thus the weighted RMS of ƒ_(p) (z₁, z₂, . . . , z_(N))and Eq. 1 may be utilized interchangeably for notational simplicityherein.

Further, if considering maximizing the PW (Process Window), one canconsider the same physical location from different PW conditions asdifferent evaluation points in the cost function in (Eq. 1). Forexample, if considering N PW conditions, then one can categorize theevaluation points according to their PW conditions and write the costfunctions as:

$\begin{matrix}{{C{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}} = {{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}} = {\sum\limits_{u = 1}^{U}{\sum\limits_{\;^{p_{u} = 1}}^{P_{u}}{w_{p_{u}}{f_{p_{u}}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z} )}}}}}} & ( {{Eq}.\mspace{11mu} 1^{\prime}} )\end{matrix}$Where ƒ_(p) _(u) (z₁, z₂, . . . , z_(N)) is the value of ƒ_(p) (z₁, z₂,. . . , z_(N)) under the u-th PW condition u=1, . . . , U. When ƒ_(p)(z₁, z₂, . . . , z_(N)) is the EPE, then minimizing the above costfunction is equivalent to minimizing the edge shift under various PWconditions, thus this leads to maximizing the PW. In particular, if thePW also consists of different mask bias, then minimizing the above costfunction also includes the minimization of MEEF (Mask Error EnhancementFactor), which is defined as the ratio between the substrate EPE and theinduced mask edge bias.

The design variables may have constraints, which can be expressed as(z₁, z₂, . . . , z_(N))∈Z, where Z is a set of possible values of thedesign variables. One possible constraint on the design variables may beimposed by a desired throughput of the lithographic projectionapparatus. The desired throughput may limit the dose and thus hasimplications for the stochastic effects (e.g., imposing a lower bound onthe stochastic effects). Higher throughput generally leads to lowerdose, shorter longer exposure time and greater stochastic effects.Consideration of substrate throughput and minimization of the stochasticeffects may constrain the possible values of the design variablesbecause the stochastic effects are function of the design variables.Without such a constraint imposed by the desired throughput, theoptimization may yield a set of values of the design variables that areunrealistic. For example, if the dose is among the design variables,without such a constraint, the optimization may yield a dose value thatmakes the throughput economically impossible. However, the usefulness ofconstraints should not be interpreted as a necessity. The throughput maybe affected by the failure rate based adjustment to parameters of thepatterning process. It is desirable to have lower failure rate of thefeature while maintaining a high throughput. Throughput may also beaffected by the resist chemistry. Slower resist (e.g., a resist thatrequires higher amount of light to be properly exposed) leads to lowerthroughput. Thus, based on the optimization process involving failurerate of a feature due to resist chemistry or fluctuations, and doserequirements for higher throughput, appropriate parameters of thepatterning process may be determined.

The optimization process therefore is to find a set of values of thedesign variables, under the constraints (z₁, z₂, . . . , z_(N))∈Z, thatminimize the cost function, i.e., to find

$\begin{matrix}{( {{\overset{\sim}{z}}_{1},{\overset{\sim}{z}}_{2},\ldots\mspace{14mu},{\overset{\sim}{z}}_{N}} ) = {{\underset{{({z_{1},\; z_{2},\;\ldots\;,z_{N}})} \in Z}{\arg\min}{{CF}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}} = {\underset{{({z_{1},z_{2},\;\ldots\;,z_{N}})} \in Z}{\arg\min}{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}\ ( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}}}}} & ( {{Eq}.\mspace{11mu} 2} )\end{matrix}$

A general method of optimizing the lithography projection apparatus,according to an embodiment, is illustrated in FIG. 11 . This methodcomprises a step 302 of defining a multi-variable cost function of aplurality of design variables. The design variables may comprise anysuitable combination selected from characteristics of the illuminationsource (300A) (e.g., pupil fill ratio, namely percentage of radiation ofthe source that passes through a pupil or aperture), characteristics ofthe projection optics (300B) and characteristics of the design layout(300C). For example, the design variables may include characteristics ofthe illumination source (300A) and characteristics of the design layout(300C) (e.g., global bias) but not characteristics of the projectionoptics (300B), which leads to an SMO. Alternatively, the designvariables may include characteristics of the illumination source (300A),characteristics of the projection optics (300B) and characteristics ofthe design layout (300C), which leads to a source-mask-lens optimization(SMLO). In step 304, the design variables are simultaneously adjusted sothat the cost function is moved towards convergence. In step 306, it isdetermined whether a predefined termination condition is satisfied. Thepredetermined termination condition may include various possibilities,i.e. the cost function may be minimized or maximized, as required by thenumerical technique used, the value of the cost function has been equalto a threshold value or has crossed the threshold value, the value ofthe cost function has reached within a preset error limit, or a presetnumber of iteration is reached. If either of the conditions in step 306is satisfied, the method ends. If none of the conditions in step 306 issatisfied, the step 304 and 306 are iteratively repeated until a desiredresult is obtained. The optimization does not necessarily lead to asingle set of values for the design variables because there may bephysical restraints caused by factors such as the failure rates, thepupil fill factor, the resist chemistry, the throughput, etc. Theoptimization may provide multiple sets of values for the designvariables and associated performance characteristics (e.g., thethroughput) and allows a user of the lithographic apparatus to pick oneor more sets.

In a lithographic projection apparatus, the source, patterning deviceand projection optics can be optimized alternatively (referred to asAlternative Optimization) or optimized simultaneously (referred to asSimultaneous Optimization). The terms “simultaneous”, “simultaneously”,“joint” and “jointly” as used herein mean that the design variables ofthe characteristics of the source, patterning device, projection opticsand/or any other design variables, are allowed to change at the sametime. The term “alternative” and “alternatively” as used herein meanthat not all of the design variables are allowed to change at the sametime.

In FIG. 11 , the optimization of all the design variables is executedsimultaneously. Such flow may be called the simultaneous flow orco-optimization flow. Alternatively, the optimization of all the designvariables is executed alternatively, as illustrated in FIG. 12 . In thisflow, in each step, some design variables are fixed while the otherdesign variables are optimized to minimize the cost function; then inthe next step, a different set of variables are fixed while the othersare optimized to minimize the cost function. These steps are executedalternatively until convergence or certain terminating conditions aremet.

As shown in the non-limiting example flowchart of FIG. 12 , first, adesign layout (step 402) is obtained, then a step of source optimizationis executed in step 404, where all the design variables of theillumination source are optimized (SO) to minimize the cost functionwhile all the other design variables are fixed. Then in the next step406, a mask optimization (MO) is performed, where all the designvariables of the patterning device are optimized to minimize the costfunction while all the other design variables are fixed. These two stepsare executed alternatively, until certain terminating conditions are metin step 408. Various termination conditions can be used, such as, thevalue of the cost function becomes equal to a threshold value, the valueof the cost function crosses the threshold value, the value of the costfunction reaches within a preset error limit, or a preset number ofiteration is reached, etc. Note that SO-MO-Alternative-Optimization isused as an example for the alternative flow. The alternative flow cantake many different forms, such as SO-LO-MO-Alternative-Optimization,where SO, LO (Lens Optimization) is executed, and MO alternatively anditeratively; or first SMO can be executed once, then execute LO and MOalternatively and iteratively; and so on. Finally, the output of theoptimization result is obtained in step 410, and the process stops.

The pattern selection algorithm, as discussed before, may be integratedwith the simultaneous or alternative optimization. For example, when analternative optimization is adopted, first a full-chip SO can beperformed, the ‘hot spots’ and/or ‘warm spots’ are identified, then anMO is performed. In view of the present disclosure numerous permutationsand combinations of sub-optimizations are possible in order to achievethe desired optimization results.

FIG. 13A shows one exemplary method of optimization, where a costfunction is minimized In step S502, initial values of design variablesare obtained, including their tuning ranges, if any. In step S504, themulti-variable cost function is set up. In step S506, the cost functionis expanded within a small enough neighborhood around the starting pointvalue of the design variables for the first iterative step (i=0). Instep S508, standard multi-variable optimization techniques are appliedto minimize the cost function. Note that the optimization problem canapply constraints, such as tuning ranges, during the optimizationprocess in S508 or at a later stage in the optimization process. StepS520 indicates that each iteration is done for the given test patterns(also known as “gauges”) for the identified evaluation points that havebeen selected to optimize the lithographic process. In step S510, alithographic response is predicted. In step S512, the result of stepS510 is compared with a desired or ideal lithographic response valueobtained in step S522. If the termination condition is satisfied in stepS514, i.e. the optimization generates a lithographic response valuesufficiently close to the desired value, and then the final value of thedesign variables is outputted in step S518. The output step may alsoinclude outputting other functions using the final values of the designvariables, such as outputting a wavefront aberration-adjusted map at thepupil plane (or other planes), an optimized source map, and optimizeddesign layout etc. If the termination condition is not satisfied, thenin step S516, the values of the design variables is updated with theresult of the i-th iteration, and the process goes back to step S506.The process of FIG. 13A is elaborated in details below.

In an exemplary optimization process, no relationship between the designvariables (z₁, z₂, . . . , z_(N)) and ƒ_(p)(z₁, z₂, . . . , z_(N)) isassumed or approximated, except that ƒ_(p)(z₁, z₂, . . . , z_(N)) issufficiently smooth (e.g. first order derivatives

$\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}},( {{n = 1},2,{\ldots\mspace{14mu} N}} )$exist), which is generally valid in a lithographic projection apparatus.An algorithm, such as the Gauss-Newton algorithm, theLevenberg-Marquardt algorithm, the gradient descent algorithm, simulatedannealing, the genetic algorithm, can be applied to find ({tilde over(z)}₁, {tilde over (z)}₂, . . . , {tilde over (z)}_(N)).

Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newtonalgorithm is an iterative method applicable to a general non-linearmulti-variable optimization problem. In the i-th iteration wherein thedesign variables (z₁, z₂, . . . , z_(N)) take values of (z_(1i), z_(2i),. . . , z_(Ni)) the Gauss-Newton algorithm linearizes ƒ_(p) (z₁, z₂, . .. , z_(N)) in the vicinity of (z_(1i), z_(2i), . . . , z_(Ni)), and thencalculates values (z_(1(i+1)), z_(2(i+1)), . . . , z_(N(i+1))) in thevicinity of (z_(1i), z_(2i), . . . , z_(Ni)) that give a minimum of CF(z₁, z₂, . . . , z_(N)). The design variables (z₁, z₂, . . . , z_(N))take the values of (z_(1(i+1)), z_(2(i+1)), . . . , z_(N(i+1))) in the(i+1)-th iteration. This iteration continues until convergence (i.e. CF(z₁, z₂, . . . , z_(N)) does not reduce any further) or a preset numberof iterations is reached.

Specifically, in the i-th iteration, in the vicinity of (z_(1i), z_(2i),. . . , z_(Ni)),

$\begin{matrix}{{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )} \approx {{f_{p}( {z_{1i},z_{2i},\ldots\mspace{14mu},z_{Ni}} )} + {{\quad{\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}}_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\;,{z_{N} = z_{Ni}},}( {z_{n} - z_{ni}} )}}} & ( {{Eq}.\mspace{14mu} 3} )\end{matrix}$

Under the approximation of Eq. 3, the cost function becomes:

                                                                                   (Eq.  4)${C{F( {z_{1},z_{2},\ldots\mspace{14mu},Z_{N}} )}} = {{\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},Z_{N}} )}}} = {\sum\limits_{p = 1}^{P}{{w_{p}( {{f_{p}( {z_{1i},z_{2i},\ldots\mspace{14mu},z_{Ni}} )} + {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}} }_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\;,{z_{N} = z_{{Ni},}}}( {z_{n} - z_{ni}} )}}}$which is a quadratic function of the design variables (z₁, z₂, . . . ,z_(N)). Every term is constant except the design variables (z₁, z₂, . .. , z_(N)).

If the design variables (z₁, z₂, . . . , z_(N)) are not under anyconstraints, (z_(1(i+1)), z_(2(i+1)), . . . , z_(N(i+1))) can be derivedby solving by N linear equations:

${\frac{{\partial C}{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}} = 0},$wherein n=1, 2, . . . N.

If the design variables (z₁, z₂, . . . , z_(N)) are under theconstraints in the form of J inequalities (e.g. tuning ranges of (z₁,z₂, . . . , z_(N)))

${{\sum\limits_{n = 1}^{N}{A_{nj}z_{n}}} \leq B_{j}},$for j=1, 2, . . . J; and K equalities (e.g. interdependence between thedesign variables)

${{\sum\limits_{n = 1}^{N}{C_{nk}z_{n}}} = D_{k}},$for k=1, 2, . . . K; the optimization process becomes a classicquadratic programming problem, wherein A_(nj), B_(j), C_(nk), D_(k) areconstants. Additional constraints can be imposed for each iteration. Forexample, a “damping factor” Δ_(D) can be introduced to limit thedifference between (z_(1(i+1)), z_(2(i+1)), . . . , z_(N(i+1))) and(z_(1i), z_(2i), . . . , z_(Ni)), so that the approximation of Eq. 3holds. Such constraints can be expressed asz_(ni)−Δ_(D)≤z_(n)≤z_(ni)+Δ_(D). (z_(1(i+1)), z_(2(i+1)), . . . ,z_(N(i+1))) can be derived using, for example, methods described inNumerical Optimization (2^(nd) ed.) by Jorge Nocedal and Stephen J.Wright (Berlin N.Y.: Vandenberghe. Cambridge University Press).

Instead of minimizing the RMS of ƒ_(p) (z₁, z₂, . . . , z_(N)), theoptimization process can minimize magnitude of the largest deviation(the worst defect) among the evaluation points to their intended values.In this approach, the cost function can alternatively be expressed as

$\begin{matrix}{{{C{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}} = {\max\limits_{1 \leq p \leq P}\frac{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}{CL_{p}}}},} & ( {{Eq}.\mspace{14mu} 5} )\end{matrix}$wherein CL_(p) is the maximum allowed value for ƒ_(p) (z₁, z₂, . . . ,z_(N)). This cost function represents the worst defect among theevaluation points. Optimization using this cost function minimizesmagnitude of the worst defect. An iterative greedy algorithm can be usedfor this optimization.

The cost function of Eq. 5 can be approximated as:

$\begin{matrix}{{{C{F( {z_{1},z_{2},\ldots\mspace{14mu},\ z_{N}} )}} = {\sum\limits_{p = 1}^{P}( \frac{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}{CL_{p}} )^{q}}},} & ( {{Eq}.\mspace{14mu} 6} )\end{matrix}$wherein q is an even positive integer such as at least 4, preferably atleast 10. Eq. 6 mimics the behavior of Eq. 5, while allowing theoptimization to be executed analytically and accelerated by usingmethods such as the deepest descent method, the conjugate gradientmethod, etc.

Minimizing the worst defect size can also be combined with linearizingof ƒ_(p) (z₁, z₂, . . . , z_(N)). Specifically, ƒ_(p) (z₁, z₂, . . . ,z_(N)) is approximated as in Eq. 3. Then the constraints on worst defectsize are written as inequalities E_(Lp)≤ƒ_(p) (z₁, z₂, . . . ,z_(N))≤E_(Up), wherein E_(Lp) and E_(Up) are two constants specifyingthe minimum and maximum allowed deviation for the ƒ_(p) (z₁, z₂, . . . ,z_(N)). Plugging Eq. 3 in, these constraints are transformed to, forp=1, . . . P,

${{\mspace{700mu}{( {{Eq}.\mspace{14mu} 6^{\prime}} ){\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}}}_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\;,{z_{N} = z_{{Ni},}}}z_{n}} \leq {E_{Up} + {{\quad{\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}}_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\;,{z_{N} = z_{{Ni},}}}{\quad{z_{ni} - {{f_{p}( {z_{1i},z_{2i},\ldots\mspace{14mu},z_{Ni}} )}\mspace{14mu}{and}\mspace{695mu}( {{Eq}.\mspace{14mu} 6^{''}} )} - {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}}}_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\;,{z_{N} = z_{Ni}},}z_{n}}} \leq {{{- {\quad{E_{Up} - {\sum\limits_{n = 1}^{N}\frac{\partial{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}{\partial z_{n}}}}}_{{z_{1} = {{z_{{1i},}z_{2}} = {z_{{2i},}\ldots}}}\mspace{11mu},{z_{N} = z_{{Ni},}}}}z_{ni}} + {f_{p}( {z_{1i},z_{2i},\ldots\mspace{14mu},z_{Ni}} )}}$

Since Eq. 3 is generally valid only in the vicinity of (z_(1i), z_(2i),. . . , z_(Ni)), in case the desired constraints E_(Lp)≤ƒ_(p) (z₁, z₂, .. . , z_(N))≤E_(Up) cannot be achieved in such vicinity, which can bedetermined by any conflict among the inequalities, the constants E_(Lp)and E_(Up) can be relaxed until the constraints are achievable. Thisoptimization process minimizes the worst defect size in the vicinity of(z_(1i), z_(2i), . . . , z_(Ni)). Then each step reduces the worstdefect size gradually, and each step is executed iteratively untilcertain terminating conditions are met. This will lead to optimalreduction of the worst defect size.

Another way to minimize the worst defect is to adjust the weight w_(p)in each iteration. For example, after the i-th iteration, if the r-thevaluation point is the worst defect, w_(r) can be increased in the(i+1)-th iteration so that the reduction of that evaluation point'sdefect size is given higher priority.

In addition, the cost functions in Eq. 4 and Eq. 5 can be modified byintroducing a Lagrange multiplier to achieve compromise between theoptimization on RMS of the defect size and the optimization on the worstdefect size, i.e.,

$\begin{matrix}{{C{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}} = {{( {1 - \lambda} ){\sum\limits_{p = 1}^{P}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}}}} + {\lambda\max\limits_{1 \leq p \leq P}\frac{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N}} )}{CL_{p}}}}} & ( {{Eq}.\mspace{11mu} 6^{\prime\prime\prime}} )\end{matrix}$where λ is a preset constant that specifies the trade-off between theoptimization on RMS of the defect size and the optimization on the worstdefect size. In particular, if λ=0, then this becomes Eq. 4 and the RMSof the defect size is only minimized; while if λ=1, then this becomesEq. 5 and the worst defect size is only minimized; if 0<λ<1, then bothare taken into consideration in the optimization. Such optimization canbe solved using multiple methods. For example, the weighting in eachiteration may be adjusted, similar to the one described previously.Alternatively, similar to minimizing the worst defect size frominequalities, the inequalities of Eq. 6′ and 6″ can be viewed asconstraints of the design variables during solution of the quadraticprogramming problem. Then, the bounds on the worst defect size can berelaxed incrementally or increase the weight for the worst defect sizeincrementally, compute the cost function value for every achievableworst defect size, and choose the design variable values that minimizethe total cost function as the initial point for the next step. By doingthis iteratively, the minimization of this new cost function can beachieved.

Optimizing a lithographic projection apparatus can expand the processwindow. A larger process window provides more flexibility in processdesign and chip design. The process window can be defined as a set offocus and dose values for which the resist image are within a certainlimit of the design target of the resist image. Note that all themethods discussed here may also be extended to a generalized processwindow definition that can be established by different or additionalbase parameters in addition to exposure dose and defocus. These mayinclude, but are not limited to, optical settings such as NA, sigma,aberrations, polarization, or optical constants of the resist layer. Forexample, as described earlier, if the PW also consists of different maskbias, then the optimization includes the minimization of MEEF (MaskError Enhancement Factor), which is defined as the ratio between thesubstrate EPE and the induced mask edge bias. The process window definedon focus and dose values only serve as an example in this disclosure. Amethod of maximizing the process window, according to an embodiment, isdescribed below.

In a first step, starting from a known condition (ƒ₀, ε₀) in the processwindow, wherein ƒ₀ is a nominal focus and ε₀ is a nominal dose,minimizing one of the cost functions below in the vicinity (ƒ₀±Δƒ,ε₀±Δε):

                                        (Eq.  7)${C{F( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f_{0},ɛ_{0}} )}} = {\max\limits_{{({f,ɛ})} = {({{f_{0} \pm {\Delta\; f}},{ɛ_{0} \pm {\Delta\; ɛ}}})}}{\max\limits_{p}{{{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f,ɛ} )}}.\mspace{79mu}{or}}}}$                                        (Eq.  7^(′))${{CF}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f_{0},ɛ_{0}} )} = {\sum\limits_{{({f,ɛ})} = {({{f_{0} \pm {\Delta\; f}},{ɛ_{0} \pm {\Delta\; ɛ}}})}}{\sum\limits_{p}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f,ɛ} )}}}}$     or                                         (Eq.  7^(″))${{CF}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f_{0},ɛ_{0}} )} = {{( {1 - \lambda} ){\sum\limits_{{({f,ɛ})} = {({{f_{0} \pm {\Delta\; f}},{ɛ_{0} \pm {\Delta\; ɛ}}})}}{\sum\limits_{p}{w_{p}{f_{p}^{2}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f,ɛ} )}}}}} + {\lambda{\max\limits_{{({f,ɛ})} = {({{f_{0} \pm {\Delta\; f}},{ɛ_{0} \pm {\Delta\; ɛ}}})}}{\max\limits_{p}{{f_{p}( {z_{1},z_{2},\ldots\mspace{14mu},z_{N},f,ɛ} )}}}}}}$

If the nominal focus ƒ₀ and nominal dose ε₀ are allowed to shift, theycan be optimized jointly with the design variables (z₁, z₂, . . . ,z_(N)). In the next step, (ƒ₀±Δƒ, ε₀±Δε) is accepted as part of theprocess window, if a set of values of (z₁, z₂, . . . , z_(N), ƒ, ε) canbe found such that the cost function is within a preset limit.

Alternatively, if the focus and dose are not allowed to shift, thedesign variables (z₁, z₂, . . . , z_(N)) are optimized with the focusand dose fixed at the nominal focus ƒ₀ and nominal dose ε₀. In analternative embodiment, (ƒ₀±Δƒ, ε₀±Δε) is accepted as part of theprocess window, if a set of values of (z₁, z₂, . . . , z_(N)) can befound such that the cost function is within a preset limit.

The methods described earlier in this disclosure can be used to minimizethe respective cost functions of Eqs. 7, 7′, or 7″. If the designvariables are characteristics of the projection optics, such as theZernike coefficients, then minimizing the cost functions of Eqs. 7, 7′,or 7″ leads to process window maximization based on projection opticsoptimization, i.e., LO. If the design variables are characteristics ofthe source and patterning device in addition to those of the projectionoptics, then minimizing the cost function of Eqs. 7, 7′, or 7″ leads toprocess window maximizing based on SMLO, as illustrated in FIG. 11 . Ifthe design variables are characteristics of the source and patterningdevice and, then minimizing the cost functions of Eqs. 7, 7′, or 7″leads to process window maximization based on SMO. The cost functions ofEqs. 7, 7′, or 7″ can also include at least one ƒ_(p) (z₁, z₂, . . . ,z_(N)) such as that in Eq. 7 or Eq. 8, that is a function of one or morestochastic effects such as the LWR or local CD variation of 2D features,and throughput.

FIG. 14 shows one specific example of how a simultaneous SMLO processcan use a Gauss Newton Algorithm for optimization. In step S702,starting values of design variables are identified. Tuning ranges foreach variable may also be identified. In step S704, the cost function isdefined using the design variables. In step S706 cost function isexpanded around the starting values for all evaluation points in thedesign layout. In optional step S710, a full-chip simulation is executedto cover all critical patterns in a full-chip design layout. Desiredlithographic response metric (such as CD or EPE) is obtained in stepS714, and compared with predicted values of those quantities in stepS712. In step S716, a process window is determined. Steps S718, S720,and S722 are similar to corresponding steps S514, S516 and S518, asdescribed with respect to FIG. 13A. As mentioned before, the finaloutput may be a wavefront aberration map in the pupil plane, optimizedto produce the desired imaging performance. The final output may also bean optimized source map and/or an optimized design layout.

FIG. 13B shows an exemplary method to optimize the cost function wherethe design variables (z₁, z₂, . . . , z_(N)) include design variablesthat may only assume discrete values.

The method starts by defining the pixel groups of the illuminationsource and the patterning device tiles of the patterning device (step802). Generally, a pixel group or a patterning device tile may also bereferred to as a division of a lithographic process component. In oneexemplary approach, the illumination source is divided into 117 pixelgroups, and 94 patterning device tiles are defined for the patterningdevice, substantially as described above, resulting in a total of 211divisions.

In step 804, a lithographic model is selected as the basis forphotolithographic simulation. Photolithographic simulations produceresults that are used in calculations of photolithographic metrics, orresponses. A particular photolithographic metric is defined to be theperformance metric that is to be optimized (step 806). In step 808, theinitial (pre-optimization) conditions for the illumination source andthe patterning device are set up. Initial conditions include initialstates for the pixel groups of the illumination source and thepatterning device tiles of the patterning device such that referencesmay be made to an initial illumination shape and an initial patterningdevice pattern. Initial conditions may also include mask bias, NA, andfocus ramp range. Although steps 802, 804, 806, and 808 are depicted assequential steps, it will be appreciated that in other embodiments ofthe invention, these steps may be performed in other sequences.

In step 810, the pixel groups and patterning device tiles are ranked.Pixel groups and patterning device tiles may be interleaved in theranking Various ways of ranking may be employed, including: sequentially(e.g., from pixel group 1 to pixel group 117 and from patterning devicetile 1 to patterning device tile 94), randomly, according to thephysical locations of the pixel groups and patterning device tiles(e.g., ranking pixel groups closer to the center of the illuminationsource higher), and according to how an alteration of the pixel group orpatterning device tile affects the performance metric.

Once the pixel groups and patterning device tiles are ranked, theillumination source and patterning device are adjusted to improve theperformance metric (step 812). In step 812, each of the pixel groups andpatterning device tiles are analyzed, in order of ranking, to determinewhether an alteration of the pixel group or patterning device tile willresult in an improved performance metric. If it is determined that theperformance metric will be improved, then the pixel group or patterningdevice tile is accordingly altered, and the resulting improvedperformance metric and modified illumination shape or modifiedpatterning device pattern form the baseline for comparison forsubsequent analyses of lower-ranked pixel groups and patterning devicetiles. In other words, alterations that improve the performance metricare retained. As alterations to the states of pixel groups andpatterning device tiles are made and retained, the initial illuminationshape and initial patterning device pattern changes accordingly, so thata modified illumination shape and a modified patterning device patternresult from the optimization process in step 812.

In other approaches, patterning device polygon shape adjustments andpairwise polling of pixel groups and/or patterning device tiles are alsoperformed within the optimization process of 812.

In an alternative embodiment the interleaved simultaneous optimizationprocedure may include to alter a pixel group of the illumination sourceand if an improvement of the performance metric is found, the dose isstepped up and down to look for further improvement. In a furtheralternative embodiment, the stepping up and down of the dose orintensity may be replaced by a bias change of the patterning devicepattern to look for further improvement in the simultaneous optimizationprocedure.

In step 814, a determination is made as to whether the performancemetric has converged. The performance metric may be considered to haveconverged, for example, if little or no improvement to the performancemetric has been witnessed in the last several iterations of steps 810and 812. If the performance metric has not converged, then the steps of810 and 812 are repeated in the next iteration, where the modifiedillumination shape and modified patterning device from the currentiteration are used as the initial illumination shape and initialpatterning device for the next iteration (step 816).

The optimization methods described above may be used to increase thethroughput of the lithographic projection apparatus. For example, thecost function may include an ƒ_(p) (z₁, z₂, . . . , z_(N)) that is afunction of the exposure time. Optimization of such a cost function ispreferably constrained or influenced by a measure of the stochasticeffects or other metrics. Specifically, a computer-implemented methodfor increasing a throughput of a lithographic process may includeoptimizing a cost function that is a function of one or more stochasticeffects of the lithographic process and a function of an exposure timeof the substrate, in order to minimize the exposure time.

In one embodiment, the cost function includes at least one ƒ_(p) (z₁,z₂, . . . , z_(N)) that is a function of one or more stochastic effects.The stochastic effects may include the failure of a feature, LWR orlocal CD variation of 2D features. In one embodiment, the stochasticeffects include stochastic variations of characteristics of a resistimage. For example, such stochastic variations may include failure rateof a feature, line edge roughness (LER), line width roughness (LWR) andcritical dimension uniformity (CDU). Including stochastic variations inthe cost function allows finding values of design variables thatminimize the stochastic variations, thereby reducing risk of defects dueto stochastic effects.

In an embodiment, there is provided a method for determining a componentof optical characteristic of a patterning process. The method involvesobtaining (i) a plurality of desired features, (ii) a plurality ofsimulated features based on the plurality of desired features and anoptical characteristic of the patterning process, and (iii) aperformance metric related to a desired feature of the plurality ofdesired features and an associated simulated feature of the plurality ofsimulated features; determining a set of optical sensitivities of thepatterning process by computing a change in value of the performancemetric based on a change in value of the optical characteristic; andidentifying, based on the set of optical sensitivities, a set ofcomponents of the optical characteristic that comprise dominantcontributors in changing the value of the performance metric.

In an embodiment, the identifying the set of components of the opticalcharacteristic involves performing a principal component analysis on theset of optical sensitivities; and determining a linear combination ofthe optical characteristic that accounts for substantial variationswithin the set of optical sensitivities.

In an embodiment, the dominant contributors comprise the linearcombination of the optical characteristic.

In an embodiment, the optical characteristic characterizes an opticalaberration of an optical system of the patterning apparatus.

In an embodiment, the optical characteristic is defined by a Zernikepolynomial.

In an embodiment, a component of the set of components of the opticalcharacteristic is a coefficient of the Zernike polynomial.

In an embodiment, the component corresponds to a correctable Zernikecoefficient, wherein the correctable Zernike coefficient is tunable viaan adjustment mechanism of the patterning apparatus.

In an embodiment, the linear combination includes a correctable Zernikecoefficient and a non-correctable Zernike coefficient, wherein thenon-correctable Zernike coefficient is not tunable via an adjustmentmechanism of the patterning apparatus.

In an embodiment, the correctable Zernike coefficient is a low orderZernike coefficient.

In an embodiment, the computing the change in the performance metricinvolves overlapping the desired feature and the simulated feature; andmeasuring a difference in a particular direction between overlappingcontours of the desired feature and the simulated feature.

In an embodiment, the difference is measured in a horizontal directionand/or a vertical direction.

In an embodiment, the obtaining the plurality of desired featuresinvolves simulating a patterning process model with an ideal opticalcharacteristic and perturbing values of a process parameter, wherein theideal optical characteristic comprises no optical aberration.

In an embodiment, the obtaining the plurality of simulated featuresinvolves simulating the patterning process model with the plurality ofdesired features and by perturbing values related to the opticalcharacteristics and the values of the process parameter to obtain theplurality of simulated features associated with the plurality of desiredfeatures.

In an embodiment, the process parameter is at least one of dose and/orfocus.

In an embodiment, the method further involves adjusting, via anadjusting mechanism, one or more mirrors of the patterning apparatusbased on the set of components of the optical characteristic to improvea performance metric of the patterning process.

In an embodiment, the adjusting the one or more mirrors involvesobtaining an optical correction potential of the patterning apparatus,wherein the correction potential is a relationship between Zernikecoefficients and orders that are correctable or non-correctable via theadjusting mechanism of the patterning apparatus; identifying mirrors ofthe optical system of the patterning apparatus corresponding to thecorrectable Zernike coefficients within the set of components of theoptical characteristic; and manipulating the identified mirrors tocompensate for effects of the non-correctable Zernike coefficients suchthat the performance metric of the patterning process is improved.

In an embodiment, the performance metric is at least one of an edgeplacement error, critical dimension, and/or displacement between edgesof two features on a substrate.

Furthermore, in an embodiment, there is provided a method of source maskoptimization based on optical sensitivity of a patterning process. Themethod involves obtaining (i) a set of optical sensitivities, and (ii) aset of components including an optical characteristic that are dominantcontributors to variations in the set of optical sensitivities;determining, via a patterning process model, source pattern or maskpattern based on the set of components including the opticalcharacteristic such that a performance metric of the patterning processis improved.

In an embodiment, the determining the source pattern or the mask patternis an iterative process. An iteration involves simulating the patterningprocess model with the set of components including the opticalcharacteristic and perturbing a parameter related to the source patternand/or the mask pattern; determining the performance metric based on thesimulation results; determining values of the parameter related to thesource pattern and/or the mask pattern such that the performance metricis improved.

In an embodiment, the performance metric is at least one of an edgeplacement error, critical dimension, and/or displacement between edgesof two features on a substrate.

In an embodiment, the improving of the performance metric comprisesminimizing the edge placement error.

In an embodiment, the patterning process model is a source model, a maskmodel, an optics model, a resist model, and/or an etch model.

In an embodiment, the parameter of the source model is at least one ofan illumination mode, and intensity.

In an embodiment, the parameter of the mask model is at least one of: aplacement location of an assist feature, a size of the feature, a shapeof the assist feature, and/or a distance between two assist features.

Furthermore, in an embodiment, there is provided a computer programproduct comprising a non-transitory computer readable medium havinginstructions recorded thereon, the instructions when executed by acomputer system implementing the aforementioned methods.

FIG. 15 is a block diagram that illustrates a computer system 100 whichcan assist in implementing the optimization methods and flows disclosedherein. Computer system 100 includes a bus 102 or other communicationmechanism for communicating information, and a processor 104 (ormultiple processors 104 and 105) coupled with bus 102 for processinginformation. Computer system 100 also includes a main memory 106, suchas a random access memory (RAM) or other dynamic storage device, coupledto bus 102 for storing information and instructions to be executed byprocessor 104. Main memory 106 also may be used for storing temporaryvariables or other intermediate information during execution ofinstructions to be executed by processor 104. Computer system 100further includes a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, is provided and coupled to bus 102 for storinginformation and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device 114,including alphanumeric and other keys, is coupled to bus 102 forcommunicating information and command selections to processor 104.Another type of user input device is cursor control 116, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 104 and for controllingcursor movement on display 112. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane. Atouch panel (screen) display may also be used as an input device.

According to one embodiment, portions of a process described herein maybe performed by computer system 100 in response to processor 104executing one or more sequences of one or more instructions contained inmain memory 106. Such instructions may be read into main memory 106 fromanother computer-readable medium, such as storage device 110. Executionof the sequences of instructions contained in main memory 106 causesprocessor 104 to perform the process steps described herein. One or moreprocessors in a multi-processing arrangement may also be employed toexecute the sequences of instructions contained in main memory 106. Inalternative embodiments, hard-wired circuitry may be used in place of orin combination with software instructions. Thus, embodiments are notlimited to any specific combination of hardware circuitry and software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 110. Volatile media include dynamic memory, such asmain memory 106. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio frequency (RF) and infrared (IR)data communications. Common forms of computer-readable media include,for example, a floppy disk, a flexible disk, hard disk, magnetic tape,any other magnetic medium, a CD-ROM, DVD, any other optical medium,punch cards, paper tape, any other physical medium with patterns ofholes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave as described hereinafter, or any other mediumfrom which a computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 100 canreceive the data on the telephone line and use an infrared transmitterto convert the data to an infrared signal. An infrared detector coupledto bus 102 can receive the data carried in the infrared signal and placethe data on bus 102. Bus 102 carries the data to main memory 106, fromwhich processor 104 retrieves and executes the instructions. Theinstructions received by main memory 106 may optionally be stored onstorage device 110 either before or after execution by processor 104.

Computer system 100 may also include a communication interface 118coupled to bus 102. Communication interface 118 provides a two-way datacommunication coupling to a network link 120 that is connected to alocal network 122. For example, communication interface 118 may be anintegrated services digital network (ISDN) card or a modem to provide adata communication connection to a corresponding type of telephone line.As another example, communication interface 118 may be a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface 118 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 120 typically provides data communication through one ormore networks to other data devices. For example, network link 120 mayprovide a connection through local network 122 to a host computer 124 orto data equipment operated by an Internet Service Provider (ISP) 126.ISP 126 in turn provides data communication services through theworldwide packet data communication network, now commonly referred to asthe “Internet” 128. Local network 122 and Internet 128 both useelectrical, electromagnetic or optical signals that carry digital datastreams. The signals through the various networks and the signals onnetwork link 120 and through communication interface 118, which carrythe digital data to and from computer system 100, are exemplary forms ofcarrier waves transporting the information.

Computer system 100 can send messages and receive data, includingprogram code, through the network(s), network link 120, andcommunication interface 118. In the Internet example, a server 130 mighttransmit a requested code for an application program through Internet128, ISP 126, local network 122 and communication interface 118. Inaccordance with one or more embodiments, one such downloaded applicationprovides for the illumination optimization of the embodiment, forexample. The received code may be executed by processor 104 as it isreceived, and/or stored in storage device 110, or other non-volatilestorage for later execution. In this manner, computer system 100 mayobtain application code in the form of a carrier wave.

FIG. 16 schematically depicts another exemplary lithographic projectionapparatus LA that includes:

-   -   a source collector module SO to provide radiation.    -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. EUV radiation) from the source        collector module SO.    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask or a reticle) MA and        connected to a first positioner PM configured to accurately        position the patterning device;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate; and    -   a projection system (e.g. a reflective projection system) PS        configured to project a pattern imparted to the radiation beam B        by patterning device MA onto a target portion C (e.g. comprising        one or more dies) of the substrate W.

As here depicted, the apparatus LA is of a reflective type (e.g.employing a reflective mask). It is to be noted that because mostmaterials are absorptive within the EUV wavelength range, the patterningdevice may have multilayer reflectors comprising, for example, amulti-layer stack of molybdenum and silicon. In one example, themulti-stack reflector has a 40 layer pairs of Molybdenum and Siliconwhere the thickness of each layer is a quarter wavelength. Even smallerwavelengths may be produced with X-ray lithography. Since most materialis absorptive at EUV and x-ray wavelengths, a thin piece of patternedabsorbing material on the patterning device topography (e.g., a TaNabsorber on top of the multi-layer reflector) defines where featureswould print (positive resist) or not print (negative resist).

Referring to FIG. 16 , the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods toproduce EUV radiation include, but are not necessarily limited to,converting a material into a plasma state that has at least one element,e.g., xenon, lithium or tin, with one or more emission lines in the EUVrange. In one such method, often termed laser produced plasma (“LPP”)the plasma can be produced by irradiating a fuel, such as a droplet,stream or cluster of material having the line-emitting element, with alaser beam. The source collector module SO may be part of an EUVradiation system including a laser, not shown in FIG. 16 , for providingthe laser beam exciting the fuel. The resulting plasma emits outputradiation, e.g., EUV radiation, which is collected using a radiationcollector, disposed in the source collector module. The laser and thesource collector module may be separate entities, for example when a CO2laser is used to provide the laser beam for fuel excitation.

In such cases, the laser is not considered to form part of thelithographic apparatus and the radiation beam is passed from the laserto the source collector module with the aid of a beam delivery systemcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the radiation source may be an integral part ofthe source collector module, for example when the radiation source is adischarge produced plasma EUV generator, often termed as a DPP radiationsource.

The illuminator IL may comprise an adjuster for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as facetted field and pupilmirror devices. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., mask table) MT, and ispatterned by the patterning device. After being reflected from thepatterning device (e.g. mask) MA, the radiation beam B passes throughthe projection system PS, which focuses the beam onto a target portion Cof the substrate W. With the aid of the second positioner PW andposition sensor PS2 (e.g. an interferometric device, linear encoder orcapacitive sensor), the substrate table WT can be moved accurately, e.g.so as to position different target portions C in the path of theradiation beam B. Similarly, the first positioner PM and anotherposition sensor PS1 can be used to accurately position the patterningdevice (e.g. mask) MA with respect to the path of the radiation beam B.Patterning device (e.g. mask) MA and substrate W may be aligned usingpatterning device alignment marks M1, M2 and substrate alignment marksP1, P2.

The depicted apparatus LA could be used in at least one of the followingmodes:

1. In step mode, the support structure (e.g. mask table) MT and thesubstrate table WT are kept essentially stationary, while an entirepattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X and/or Y direction so that a differenttarget portion C can be exposed.

2. In scan mode, the support structure (e.g. mask table) MT and thesubstrate table WT are scanned synchronously while a pattern imparted tothe radiation beam is projected onto a target portion C (i.e. a singledynamic exposure). The velocity and direction of the substrate table WTrelative to the support structure (e.g. mask table) MT may be determinedby the (de-)magnification and image reversal characteristics of theprojection system PS.

3. In another mode, the support structure (e.g. mask table) MT is keptessentially stationary holding a programmable patterning device, and thesubstrate table WT is moved or scanned while a pattern imparted to theradiation beam is projected onto a target portion C. In this mode,generally a pulsed radiation source is employed and the programmablepatterning device is updated as required after each movement of thesubstrate table WT or in between successive radiation pulses during ascan. This mode of operation can be readily applied to masklesslithography that utilizes programmable patterning device, such as aprogrammable mirror array of a type as referred to above.

FIG. 17 shows the apparatus LA in more detail, including the sourcecollector module SO, the illumination system IL, and the projectionsystem PS. The source collector module SO is constructed and arrangedsuch that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiationemitting plasma 210 may be formed by a discharge produced plasmaradiation source. EUV radiation may be produced by a gas or vapor, forexample Xe gas, Li vapor or Sn vapor in which the very hot plasma 210 iscreated to emit radiation in the EUV range of the electromagneticspectrum. The very hot plasma 210 is created by, for example, anelectrical discharge causing an at least partially ionized plasma.Partial pressures of, for example, 10 Pa of Xe, Li, Sn vapor or anyother suitable gas or vapor may be required for efficient generation ofthe radiation. In an embodiment, a plasma of excited tin (Sn) isprovided to produce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211. The contaminant trap 230 may include a channelstructure. Contamination trap 230 may also include a gas barrier or acombination of a gas barrier and a channel structure. The contaminanttrap or contaminant barrier 230 further indicated herein at leastincludes a channel structure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘O’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithographicapparatus. Further, there may be more mirrors present than those shownin the Figures, for example there may be 1-6 additional reflectiveelements present in the projection system PS than shown in FIG. 17 .

Collector optic CO, as illustrated in FIG. 17 , is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type is desirably usedin combination with a discharge produced plasma radiation source.

Alternatively, the source collector module SO may be part of an LPPradiation system as shown in FIG. 18 . A laser LAS is arranged todeposit laser energy into a fuel, such as xenon (Xe), tin (Sn) orlithium (Li), creating the highly ionized plasma 210 with electrontemperatures of several 10's of eV. The energetic radiation generatedduring de-excitation and recombination of these ions is emitted from theplasma, collected by a near normal incidence collector optic CO andfocused onto the opening 221 in the enclosing structure 220.

The embodiments may further be described using the following clauses:

1. A method for determining a component of optical characteristic of apatterning process, the method comprising:

obtaining (i) a plurality of desired features, (ii) a plurality ofsimulated features based on the plurality of desired features and anoptical characteristic of the patterning process, and (iii) aperformance metric related to a desired feature of the plurality ofdesired features and an associated simulated feature of the plurality ofsimulated features;

determining a set of optical sensitivities of the patterning process bycomputing a change in value of the performance metric based on a changein value of the optical characteristic; and

identifying, based on the set of optical sensitivities, a set ofcomponents of the optical characteristic that comprise dominantcontributors in changing the value of the performance metric.

2. The method of clause 1, wherein the identifying the set of componentsof the optical characteristic comprises:

performing a principal component analysis on the set of opticalsensitivities; and determining a linear combination of the opticalcharacteristic that accounts for substantial variations within the setof optical sensitivities.

3. The method of any of clauses 1-2, wherein the dominant contributorscomprise the linear combination of the optical characteristic.

4. The method of any of clauses 1-3, wherein the optical characteristiccharacterizes an optical aberration of an optical system of thepatterning apparatus.

5. The method of clause 4, wherein the optical characteristic is definedby a Zernike polynomial.

6. The method of clause 5, wherein a component of the set of componentsof the optical characteristic is a coefficient of the Zernikepolynomial.

7. The method of clause 6, wherein the component corresponds to acorrectable Zernike coefficient, wherein the correctable Zernikecoefficient is tunable via an adjustment mechanism of the patterningapparatus.

8. The method of any of clause 6-7, wherein the linear combinationincludes a correctable Zernike coefficient and a non-correctable Zernikecoefficient, wherein the non-correctable Zernike coefficient is nottunable via an adjustment mechanism of the patterning apparatus.9. The method of clause 8, wherein the correctable Zernike coefficientis a low order Zernike coefficient.10. The method of any of clauses 1-9, wherein the computing the changein the performance metric comprises:

overlapping the desired feature and the simulated feature; and

measuring a difference in a particular direction between overlappingcontours of the desired feature and the simulated feature.

11. The method of any of clauses 1-10, wherein the difference ismeasured in a horizontal direction and/or a vertical direction.

12. The method of any of clauses 1-11, wherein the obtaining theplurality of desired features comprises:

simulating a patterning process model with an ideal opticalcharacteristic and perturbing values of a process parameter, wherein theideal optical characteristic comprises no optical aberration.

13. The method of any of clauses 1-12, wherein the obtaining theplurality of simulated features comprises:

simulating the patterning process model with the plurality of desiredfeatures and by perturbing values related to the optical characteristicsand the values of the process parameter to obtain the plurality ofsimulated features associated with the plurality of desired features.

14. The method of any of clauses 12-13, wherein the process parameter isat least one of dose and/or focus.

15. The method of any of clauses 1-14, further comprising:

adjusting, via an adjusting mechanism, one or more mirrors of thepatterning apparatus based on the set of components of the opticalcharacteristic to improve a performance metric of the patterningprocess.

16. The method of clause 15, wherein the adjusting the one or moremirrors comprises:

obtaining an optical correction potential of the patterning apparatus,wherein the correction potential is a relationship between Zernikecoefficients and orders that are correctable or non-correctable via theadjusting mechanism of the patterning apparatus;

identifying mirrors of the optical system of the patterning apparatuscorresponding to the correctable Zernike coefficients within the set ofcomponents of the optical characteristic; and

manipulating the identified mirrors to compensate for effects of thenon-correctable Zernike coefficients such that the performance metric ofthe patterning process is improved.

17. The method of any of clauses 15-16, wherein the performance metricis at least one of an edge placement error, critical dimension, and/ordisplacement between edges of two features on a substrate.

18. A method of source mask optimization based on optical sensitivity ofa patterning process, the method comprising:

-   -   obtaining (i) a set of optical sensitivities, and (ii) a set of        components including an optical characteristic that are dominant        contributors to variations in the set of optical sensitivities;

determining, via a patterning process model, source pattern or maskpattern based on the set of components including the opticalcharacteristic such that a performance metric of the patterning processis improved.

19. The method of clause 18, wherein the determining the source patternor the mask pattern is an iterative process, an iteration comprises:

simulating the patterning process model with the set of componentsincluding the optical characteristic and perturbing a parameter relatedto the source pattern and/or the mask pattern;

determining the performance metric based on the simulation results;

determining values of the parameter related to the source pattern and/orthe mask pattern such that the performance metric is improved.

20. The method of any of clauses 18-16, wherein the performance metricis at least one of an edge placement error, critical dimension, and/ordisplacement between edges of two features on a substrate.

21. The method of any of clauses 18-20, wherein the improving of theperformance metric comprises minimizing the edge placement error.

22. The method of any of clauses 18-21, wherein the patterning processmodel is a source model, a mask model, an optics model, a resist model,and/or an etch model.

23. The method of any of clauses 18-22, wherein the parameter of thesource model is at least one of an illumination mode, and intensity.

24. The method of any of clauses 18-22, wherein the parameter of themask model is at least one of: a placement location of an assistfeature, a size of the feature, a shape of the assist feature, and/or adistance between two assist features.

25. A computer program product comprising a non-transitory computerreadable medium having instructions recorded thereon, the instructionswhen executed by a computer system implementing the method of any ofclauses 1-24.

The concepts disclosed herein may simulate or mathematically model anygeneric imaging system for imaging sub wavelength features, and may beespecially useful with emerging imaging technologies capable ofproducing wavelengths of an increasingly smaller size. Emergingtechnologies already in use include EUV (extreme ultra violet)lithography that is capable of producing a 193 nm wavelength with theuse of an ArF laser, and even a 157 nm wavelength with the use of aFluorine laser. Moreover, EUV lithography is capable of producingwavelengths within a range of 20-5 nm by using a synchrotron or byhitting a material (either solid or a plasma) with high energy electronsin order to produce photons within this range.

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

Although specific reference may be made in this text to the use ofembodiments in the manufacture of ICs, it should be understood that theembodiments herein may have many other possible applications. Forexample, it may be employed in the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,liquid-crystal displays (LCDs), thin film magnetic heads,micromechanical systems (MEMs), etc. The skilled artisan will appreciatethat, in the context of such alternative applications, any use of theterms “reticle”, “wafer” or “die” herein may be considered as synonymousor interchangeable with the more general terms “patterning device”,“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist) or a metrology or inspection tool.Where applicable, the disclosure herein may be applied to such and othersubstrate processing tools. Further, the substrate may be processed morethan once, for example in order to create, for example, a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

In the present document, the terms “radiation” and “beam” as used hereinencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of about 365, about 248, about 193,about 157 or about 126 nm) and extreme ultra-violet (EUV) radiation(e.g. having a wavelength in the range of 5-20 nm), as well as particlebeams, such as ion beams or electron beams.

The terms “optimizing” and “optimization” as used herein refers to ormeans adjusting a patterning apparatus (e.g., a lithography apparatus),a patterning process, etc. such that results and/or processes have moredesirable characteristics, such as higher accuracy of projection of adesign pattern on a substrate, a larger process window, etc. Thus, theterm “optimizing” and “optimization” as used herein refers to or means aprocess that identifies one or more values for one or more parametersthat provide an improvement, e.g. a local optimum, in at least onerelevant metric, compared to an initial set of one or more values forthose one or more parameters. “Optimum” and other related terms shouldbe construed accordingly. In an embodiment, optimization steps can beapplied iteratively to provide further improvements in one or moremetrics.

Aspects of the invention can be implemented in any convenient form. Forexample, an embodiment may be implemented by one or more appropriatecomputer programs which may be carried on an appropriate carrier mediumwhich may be a tangible carrier medium (e.g. a disk) or an intangiblecarrier medium (e.g. a communications signal). Embodiments of theinvention may be implemented using suitable apparatus which mayspecifically take the form of a programmable computer running a computerprogram arranged to implement a method as described herein. Thus,embodiments of the disclosure may be implemented in hardware, firmware,software, or any combination thereof. Embodiments of the disclosure mayalso be implemented as instructions stored on a machine-readable medium,which may be read and executed by one or more processors. Amachine-readable medium may include any mechanism for storing ortransmitting information in a form readable by a machine (e.g., acomputing device). For example, a machine-readable medium may includeread only memory (ROM); random access memory (RAM); magnetic diskstorage media; optical storage media; flash memory devices; electrical,optical, acoustical or other forms of propagated signals (e.g. carrierwaves, infrared signals, digital signals, etc.), and others. Further,firmware, software, routines, instructions may be described herein asperforming certain actions. However, it should be appreciated that suchdescriptions are merely for convenience and that such actions in factresult from computing devices, processors, controllers, or other devicesexecuting the firmware, software, routines, instructions, etc.

In block diagrams, illustrated components are depicted as discretefunctional blocks, but embodiments are not limited to systems in whichthe functionality described herein is organized as illustrated. Thefunctionality provided by each of the components may be provided bysoftware or hardware modules that are differently organized than ispresently depicted, for example such software or hardware may beintermingled, conjoined, replicated, broken up, distributed (e.g. withina data center or geographically), or otherwise differently organized.The functionality described herein may be provided by one or moreprocessors of one or more computers executing code stored on a tangible,non-transitory, machine readable medium. In some cases, third partycontent delivery networks may host some or all of the informationconveyed over networks, in which case, to the extent information (e.g.,content) is said to be supplied or otherwise provided, the informationmay be provided by sending instructions to retrieve that informationfrom a content delivery network.

Unless specifically stated otherwise, as apparent from the discussion,it is appreciated that throughout this specification discussionsutilizing terms such as “processing,” “computing,” “calculating,”“determining” or the like refer to actions or processes of a specificapparatus, such as a special purpose computer or a similar specialpurpose electronic processing/computing device.

The reader should appreciate that the present application describesseveral inventions. Rather than separating those inventions intomultiple isolated patent applications, these inventions have beengrouped into a single document because their related subject matterlends itself to economies in the application process. But the distinctadvantages and aspects of such inventions should not be conflated. Insome cases, embodiments address all of the deficiencies noted herein,but it should be understood that the inventions are independentlyuseful, and some embodiments address only a subset of such problems oroffer other, unmentioned benefits that will be apparent to those ofskill in the art reviewing the present disclosure. Due to costsconstraints, some inventions disclosed herein may not be presentlyclaimed and may be claimed in later filings, such as continuationapplications or by amending the present claims. Similarly, due to spaceconstraints, neither the Abstract nor the Summary sections of thepresent document should be taken as containing a comprehensive listingof all such inventions or all aspects of such inventions.

It should be understood that the description and the drawings are notintended to limit the present disclosure to the particular formdisclosed, but to the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the inventions as defined by the appended claims.

Modifications and alternative embodiments of various aspects of theinventions will be apparent to those skilled in the art in view of thisdescription. Accordingly, this description and the drawings are to beconstrued as illustrative only and are for the purpose of teaching thoseskilled in the art the general manner of carrying out the inventions. Itis to be understood that the forms of the inventions shown and describedherein are to be taken as examples of embodiments. Elements andmaterials may be substituted for those illustrated and described herein,parts and processes may be reversed or omitted, certain features may beutilized independently, and embodiments or features of embodiments maybe combined, all as would be apparent to one skilled in the art afterhaving the benefit of this description. Changes may be made in theelements described herein without departing from the spirit and scope ofthe invention as described in the following claims. Headings used hereinare for organizational purposes only and are not meant to be used tolimit the scope of the description.

As used throughout this application, the word “may” is used in apermissive sense (i.e., meaning having the potential to), rather thanthe mandatory sense (i.e., meaning must). The words “include”,“including”, and “includes” and the like mean including, but not limitedto. As used throughout this application, the singular forms “a,” “an,”and “the” include plural referents unless the content explicitlyindicates otherwise. Thus, for example, reference to “an” element or “a”element includes a combination of two or more elements, notwithstandinguse of other terms and phrases for one or more elements, such as “one ormore.” The term “or” is, unless indicated otherwise, non-exclusive,i.e., encompassing both “and” and “or.” Terms describing conditionalrelationships, e.g., “in response to X, Y,” “upon X, Y,”, “if X, Y,”“when X, Y,” and the like, encompass causal relationships in which theantecedent is a necessary causal condition, the antecedent is asufficient causal condition, or the antecedent is a contributory causalcondition of the consequent, e.g., “state X occurs upon condition Yobtaining” is generic to “X occurs solely upon Y” and “X occurs upon Yand Z.” Such conditional relationships are not limited to consequencesthat instantly follow the antecedent obtaining, as some consequences maybe delayed, and in conditional statements, antecedents are connected totheir consequents, e.g., the antecedent is relevant to the likelihood ofthe consequent occurring. Statements in which a plurality of attributesor functions are mapped to a plurality of objects (e.g., one or moreprocessors performing steps A, B, C, and D) encompasses both all suchattributes or functions being mapped to all such objects and subsets ofthe attributes or functions being mapped to subsets of the attributes orfunctions (e.g., both all processors each performing steps A-D, and acase in which processor 1 performs step A, processor 2 performs step Band part of step C, and processor 3 performs part of step C and step D),unless otherwise indicated. Further, unless otherwise indicated,statements that one value or action is “based on” another condition orvalue encompass both instances in which the condition or value is thesole factor and instances in which the condition or value is one factoramong a plurality of factors. Unless otherwise indicated, statementsthat “each” instance of some collection have some property should not beread to exclude cases where some otherwise identical or similar membersof a larger collection do not have the property, i.e., each does notnecessarily mean each and every. References to selection from a rangeincludes the end points of the range.

In the above description, any processes, descriptions or blocks inflowcharts should be understood as representing modules, segments orportions of code which include one or more executable instructions forimplementing specific logical functions or steps in the process, andalternate implementations are included within the scope of the exemplaryembodiments of the present advancements in which functions can beexecuted out of order from that shown or discussed, includingsubstantially concurrently or in reverse order, depending upon thefunctionality involved, as would be understood by those skilled in theart.

To the extent certain U.S. patents, U.S. patent applications, or othermaterials (e.g., articles) have been incorporated by reference, the textof such U.S. patents, U.S. patent applications, and other materials isonly incorporated by reference to the extent that no conflict existsbetween such material and the statements and drawings set forth herein.In the event of such conflict, any such conflicting text in suchincorporated by reference U.S. patents, U.S. patent applications, andother materials is specifically not incorporated by reference herein.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the present disclosures. Indeed, the novel methods, apparatusesand systems described herein can be embodied in a variety of otherforms; furthermore, various omissions, substitutions and changes in theform of the methods, apparatuses and systems described herein can bemade without departing from the spirit of the present disclosures. Theaccompanying claims and their equivalents are intended to cover suchforms or modifications as would fall within the scope and spirit of thepresent disclosures.

What is claimed is:
 1. A method comprising: obtaining (i) a plurality ofdesired features, (ii) a plurality of simulated features based on theplurality of desired features and an optical characteristic of apatterning process, and (iii) a performance metric related to a desiredfeature of the plurality of desired features and an associated simulatedfeature of the plurality of simulated features; determining a set ofoptical sensitivities of the patterning process by computing a change invalue of the performance metric based on a change in value of theoptical characteristic; and identifying, by a hardware computer systembased on the set of optical sensitivities, a set of one or morecomponents of the optical characteristic that comprises one or moredominant contributors in changing the value of the performance metric.2. The method of claim 1, wherein the identifying the set of one or morecomponents of the optical characteristic comprises: performing aprincipal component analysis on the set of optical sensitivities; anddetermining, from the principal component analysis, a combination of theoptical characteristic that accounts for substantial variations withinthe set of optical sensitivities.
 3. The method of claim 1, wherein theone or more dominant contributors comprise a linear combination of theoptical characteristic.
 4. The method of claim 1, wherein the opticalcharacteristic characterizes an optical aberration of an optical systemof a patterning apparatus.
 5. The method of claim 4, wherein the opticalcharacteristic is represented by a Zernike polynomial.
 6. The method ofclaim 5, wherein a component of the set of one or more components of theoptical characteristic is a coefficient of the Zernike polynomial. 7.The method of claim 6, wherein the component corresponds to acorrectable Zernike coefficient, wherein the correctable Zernikecoefficient is tunable via an adjustment mechanism of the patterningapparatus.
 8. The method of claim 6, wherein the set of one or morecomponents includes a correctable Zernike coefficient and anon-correctable Zernike coefficient, wherein the non-correctable Zernikecoefficient is not tunable via an adjustment mechanism of the patterningapparatus.
 9. The method of claim 8, wherein the correctable Zernikecoefficient is a low order Zernike coefficient.
 10. The method of claim1, wherein the computing the change in the performance metric comprises:overlapping the desired feature and the associated simulated feature;and determining a difference, in a particular direction, betweenoverlapping contours of the desired feature and the associated simulatedfeature.
 11. The method of claim 1, wherein the obtaining the pluralityof desired features comprises simulating using a patterning processmodel with an ideal optical characteristic and perturbing values of aprocess parameter, wherein the ideal optical characteristic comprises nooptical aberration, and/or wherein the obtaining the plurality ofsimulated features comprises simulating using a patterning process modelwith the plurality of desired features and perturbing values related tothe optical characteristic and of a process parameter to obtain theplurality of simulated features associated with the plurality of desiredfeatures.
 12. The method of claim 11, wherein the process parameter isdose and/or focus.
 13. The method of claim 1, further comprising:adjusting, via an adjusting mechanism, one or more mirrors of apatterning apparatus based on the set of one or more components of theoptical characteristic and based on a performance metric of thepatterning process, wherein the adjusting the one or more mirrorscomprises: obtaining an optical correction potential of the patterningapparatus, wherein the correction potential represents a relationshipbetween Zernike coefficients and orders that are correctable ornon-correctable via the adjusting mechanism of the patterning apparatus;identifying one or more mirrors of an optical system of the patterningapparatus corresponding to correctable Zernike coefficients within theset of one or more components of the optical characteristic; andmanipulating the identified one or more mirrors to compensate foreffects of non-correctable Zernike coefficients based on the performancemetric of the patterning process.
 14. The method of claim 1, wherein theperformance metric is at least one selected from: an edge placementerror, critical dimension, and/or displacement between edges of twofeatures on a substrate.
 15. A computer program product comprising anon-transitory computer readable medium having instructions therein, theinstructions, when executed by a computer system, configured to causethe computer system to at least: obtain (i) a plurality of desiredfeatures, (ii) a plurality of simulated features based on the pluralityof desired features and an optical characteristic of a patterningprocess, and (iii) a performance metric related to a desired feature ofthe plurality of desired features and an associated simulated feature ofthe plurality of simulated features; determine a set of opticalsensitivities of the patterning process by computing a change in valueof the performance metric based on a change in value of the opticalcharacteristic; and identify, based on the set of optical sensitivities,a set of one or more components of the optical characteristic thatcomprises one or more dominant contributors in changing the value of theperformance metric.
 16. The computer program product of claim 15,wherein the instructions configured to cause the computer system toidentify the set of one or more components of the optical characteristicare further configured to cause the computer system to: perform aprincipal component analysis on the set of optical sensitivities; anddetermine, from the principal component analysis, a combination of theoptical characteristic that accounts for substantial variations withinthe set of optical sensitivities.
 17. The computer program product ofclaim 15, wherein the one or more dominant contributors comprise alinear combination of the optical characteristic.
 18. The computerprogram product of claim 15, wherein the optical characteristiccharacterizes an optical aberration of an optical system of a patterningapparatus.
 19. The computer program product of claim 18, wherein theoptical characteristic is represented by a Zernike polynomial.
 20. Thecomputer program product of claim 15, wherein the performance metric isat least one selected from: an edge placement error, critical dimension,and/or displacement between edges of two features on a substrate.